Prelude: The Indo-European culture
The Indo-European family is a group of related languages now spoken on every continent on Earth. It includes most European languages along with the Indic and Iranian languages of Asia; in modern times, colonialism by Western Europeans has spread English, Spanish, French, and other Indo-European languages to almost every corner of the world.
We know very little about the original Indo-Europeans. Since no archaeological site has been identified with the Proto-Indo-European society for certain, the only evidence we have to describe their way of life is through determining which words seem to have cognates in every Indo-European branch, and thus existed in the original language. Proto-Indo-European had a word for bronze, but not iron; they had axes, spears, and knives; they had wheels, but not chariots. They raised cattle, sheep, and goats, and the flowering of Indo-European culture across Europe may have begun with the domestication of the horse. Their religion was polytheistic — in fact, it is believed that the oldest gods of later Indo-European cultures — those of the Greeks, Norse, Celts, Hindus, and other polytheistic Indo-European societies — probably corresponded to Proto-Indo-European deities. Linguistic correspondences can be discerned — the names of the Greek Ouranous and the Hindu Varuna are cognates. Jupiter, Zeus, and Dyaus Pita (a father-god mentioned in the oldest Hindu texts) are all believed to be later forms of a Proto-Indo-European sky god, *Dyeus. But nothing is known for certain about Indo-European culture; all we can determine is what can be shown from the later languages and cultures of Indo-European peoples.
No one is certain of the origins of the Indo-European family, though much progress has been made in reconstructing the family's oldest known ancestor, Proto-Indo-European. A number of different theories exist about the original homeland of the Proto-Indo-Europeans. The Kurgan Hypothesis links the Proto-Indo-Europeans with archaeological sites in the Russian steppe, near the Black Sea, inhabited from the fifth to the third millenium BCE. According to this theory, the development of agriculture and the domestication of the horse drove expansion outwards by Indo-Europeans, who settled amongst or displaced native peoples across Europe and parts of Asia. The original formulation of this hypothesis proposed an essentially military campaign in which Indo-Europeans used advanced technology to conquer the cultures that it displaced.
The more recent Anatolian Hypothesis claims Anatolia (in modern-day Turkey) as the Proto-Indo-European homeland, the source of a very gradual and peaceful spread of a Neolithic, agricultural society across Europe. This theory was put forth in the late 1980s, and though originally quite popular, it has become less so in recent years, largely because it postulates a breakup of Proto-Indo-European around 7000 BCE, far earlier than seems possible given other research.
Besides these theories, various other ones exist, many of which have a distinctly nationalistic bent; some Indian scholars maintain that the ancient Harappan Civilization was Indo-European (which is generally not considered plausible by archaeologists) and in fact that India formed the ancestral homeland of Indo-European cultures; in this theory, European branches of the language family are the result of expansion outward by ancient peoples from India. Similar Eurocentric views exist, linking Indo-European to Paleolithic European cultures, claiming that Indo-European culture originally developed across Europe rather than having been spread across it through relatively recent migration. The existence of an Indo-European language family that subsumes an enormous number of the world's languages has always been a particularly fertile ground for the formation of nationalist and even nakedly racist ideologies.
Aryans at a glance
The Aryan culture, also known as the Indo-Iranian culture, was a branch of the Indo-European culture that occupied a large territory in Central Asia, most likely continuing as a single unified culture until around 2000 BCE. The descendents of the Aryan culture are the Iranian or Persian culture, the Indo-Aryan culture, and the Nuristani culture (now confined to a small area of Afghanistan.) The term comes from the Vedic Sanskrit and Avestan (the oldest attested language of the Persians) word arya-, which came from the hypothetical Proto-Indo-European word *ar-yo-; ar- being a verb meaning 'to assemble skillfully. The name of Iran actually comes from Aryānām XšaΘra, an ancient name meaning "realm of the Aryans".
There are a number of theories linking the the Aryans to various archaeological sites in Central Asia, though no single theory has gained universal agreement. It's not known, then, precisely where they lived. The Indo-Iranians may have been the first society to develop the chariot (interestingly, the Greek word for chariot is harma, which comes from the same Proto-Indo-European *ar-.) With this important technological development, they were able to spread into Afghanistan, Iran, and northern India, even extending into Syria and Mesopotamia.
The Indo-Aryan culture, one of the offspring of the Aryan culture, developed among Aryan settlements of northern India. The oldest attestations of their language are found in the Rigveda, a collection of hymns and the first of the four Vedas, which are the most ancient of Hinduism's holy texts. The Indo-Aryans who established themselves in northern India are sometimes known as the Vedic culture and according to current historical theories brought the ancient precursor of the Hindu religion and the Sanskrit language to India. Sanskrit is the origin of many of the modern languages of India, including Hindi, Bengali, Marathi, Urdu, and numerous others (aside from English, most of India's other widely-spoken languages belong to the Dravidian family.)
The Iranian culture developed in a second expansion, taking place in the early centuries of the first millenium BCE. The Iranians took over what is now Iran — and also much of Central Asia, Ukraine, and even some of Russia. Today, Persian — a descendent of the original Iranian language — is of course still spoken in Iran, with relatives in Afghanistan and many other Central Asian countries, though they are mostly minority languages, spoken by small groups surrounded by speakers of Turkic languages.
The "Aryan Race"
The relationship between languages like Latin, Greek, and Sanskrit was observed as early as the seventeenth century, but it wasn't until the mid-nineteenth century that the basic shape of the Indo-European language family was ironed out through systematic comparisons of words. The birth of Indo-European linguistics led to the development of ideas of a distinct Indo-European culture. With the rise of scientific theories of "race" in the late nineteenth and early twentieth centuries, it was proposed that the Indo-Europeans constituted a separate race of humanity.
Further, the (European) proponents of the theory tended to believe that Indo-European culture either developed in northern Europe or that northern Europeans were the genetically "purest" Indo-Europeans. The British rulers of India found the concept useful, deliberately distorting the Aryan invasion theory to suggest that India was composed of two races, the lighter-skinned Aryans of northern India and the darker-skinned Dravidians of southern India. The Aryans then, according to the British, established themselves as the higher castes in Indian society, and thus they tied British rule of India to the caste system and to notions of the inherent superiority of Indo-European culture.
How Indo-Europeans became Aryans
The word "Aryan", originally (and legitimately) applied to the Indo-Iranian culture, became tied in nineteenth century linguistics to Indo-European culture as a whole. Max Müller (1823-1900) was a linguist who had a particular interest in Indian culture. He essentially created the concept of comparative religion, and tied his linguistic research to his efforts to discover the similarities between the religions of various Indo-European cultures. He was fascinated by the correspondences between the gods of pagan European religions and those of Hinduism, and he viewed language and religion as intimately linked together. In his work, he supposed (as many philologists of the time did) that Sanskrit was the ancient source of the Indo-European languages; thus he believed that the Aryans were the original Indo-Europeans.
Müller's work was latched onto by nationalists who explicitly contrasted "Aryan" culture with Semitic culture; while Müller himself used the term Aryan to mean nothing more than people speaking "Aryan" — that is, Indo-European — languages, others found his writings inspirational in creating imagined genetic contrasts between the Aryan and Semitic "races". Müller himself explicitly rejected racism and while he was fascinated by Indian culture, he did not believe that "Aryans" were in any way inherently superior to other people; it was his lasting sorrow that his work was used to justify such beliefs.
Nazi racial ideology
Racial ideology caught on in a big way in Germany; various pseudo-scholarly works were published to advance these ideas. In particular, the ancient Vedic civilization of northern India was linked to the ancient Germanic Goths and Vandals. The two groups were claimed to be ethnically identical (though Indians had since become contaminated from mixing with darker inferior races.) The original Aryans were thought to have been distinctly Nordic in appearance: tall, light-skinned, and ideally blond with blue eyes. The superior Aryan races were those who had forged civilization — while Jews represented a foreign, Semitic presence within Germany's Aryan society.
Adolf Hitler's Mein Kampf proposed a division of races into three categories — those that create civilization, those that can sustain but not create civilization, and those who inevitably destroy civilization. At the bottom of the heap were Jews, Gypsies, the Khoi people of Africa (Hottentots and Bushmen), and Australian Aborigines; somewhat better were the Japanese (who were imagined to be sustaining a civilization introduced by Aryans earlier in history) and southern and central Europeans, whose blood had been contaminated by mixing with that of the Moors. Marriage between Aryans and those of lesser races was prohibited, as mixing of blood inevitably resulted in the decline of the race. In Hitler's belief, it was further necessary for the lowest races to be eliminated from society entirely.
Beyond purely racial ideas, some thinkers in the Nazi Party believed further in the idea that the Indo-European people had a shared spiritual nature. They wished for the renunciation of Christianity, which they viewed as a foreign, Semitic religion, and a return to the pagan, pre-Christian beliefs of the various Indo-European tribes. Many of the Party's cultural initiatives failed to catch on, though, and this was no exception; Christianity was never formally discouraged, but an effort was made to replace Christian symbolism with pre-Christian Germanic symbolism, exemplified in the use of runes to mark the graves of SS officers. They drew much from Müller's writings establishing correspondences between the gods of different Indo-European groups. A fascination with what was perceived as authentically "Aryan" spirituality led the Nazis to adopt the swastika as their symbol, after it was discovered in the ruins of Troy and thought to be a religious symbol common to Indo-European civilization.
Nowadays the term "Aryan" is heavily loaded in the West; the term tends to be recognized far more for its racist associations than its original meaning as a term used by the Indo-Iranian culture. It's still used with its original meaning in India but in Europe and the United States the term Indo-Iranian has replaced it almost entirely in linguistic and anthropological usage, as its meaning is not contaminated with racist ideology.
Khan, Kamal. "Indo-Iranian languages." (http://stp.ling.uu.se/~kamalk/indo_iran%20lang.html)
The Indo-European Documentation Cnter at The University of Texas at Austin (http://www.utexas.edu/cola/depts/lrc/iedocctr/ie.html)
"The Indo-European Family of Languages." (http://www.krysstal.com/langfams_indoeuro.html)
Holm, Hans J. "A Possible Homeland of the Indo-European Languages." (http://www.hjholm.de/)
"The Aryans in a historical context." The Circle of Ancient Iranian Studies. (http://www.cais-soas.com/CAIS/Anthropology/er_ermazdesn.htm)
"The Myth of the 'Aryan Tribe'." (http://www.nornirsaett.de/the-myth-of-the-aryan-tribe/)
"India Through The Ages." (http://library.thinkquest.org/04oct/01368/web/html_pre_pg-3.html)