Bedouin culture flourished during the "Jahiliyya" (or the "time of ignorance" which occurred for several hundred years before the spread of Islam). Their culture has been nearly lost in recent times due to assimilation and growth of cities in the Middle East. Bedouins are pastoral nomads who were basically the original Arabs of what is now considered the Middle East. The term "Arab" used to specifically refer to Bedouins but later was extended to all Arab speaking people. The Bedouins are also known as "bedawi" in Arabic.
The Bedouins rely heavily on camels, due to the fact that the animals can handle the often high heat with no problem. Camels are transportation, a source of milk (females can lactate up to a year after giving birth and produce up to 4 liters of milk a day), and their dung can even be used as fuel for campfires. The animals can carry up to 425 pounds, and thus make traveling possible for the nomadic tribes. (The camels referred to are dromedary kind with one hump. If you ever see a picture of someone in Arabia on a camel with two humps, it is wrong.)
The Bedouin social scene consists of an elaborate network of relatives and alliances. The household for Bedouins is different from traditional households containing a nuclear family. A household consists of a compound with black tents made from black goat hides. The compound contains the extended family and all labor is split up by gender. Men are in charge of milking and watering the animals, the women are in charge of making food, packing and unpacking the tent, and making and mending the tents.
Bedouins are known for their amazing hospitality. Honor and reputation are the most important things any Bedouin has, as well as their lineage. Men can gain honor by being hospitable and helping even random people that would come by. The Bedouin culture is governed by strict rules. Due to the limited resources of their environment, there are even rules for camel raiding. If one tribe decides to raid the camels from another tribe, there are certain rules about what is appropriate and what would make one lose or gain honor.
Bedouin families are based on a patriarchial system and tribal networks are based on kin groups that go way back. Marriage with matrilineal cousins is preferred to keep family lines clean. Tribes are formed by 5 generations of matrilineal relatives. Groups also make alliances with other groups and everyone is very aware of their own lineage. Many relatives are referred to as cousins, even if the relationship is not a technical cousin. If someone is related to someone 27 generations back, they may still be considered a cousin.
Bedouins had polyandry and polygamy in families, marrying a single partner wasn't always done. They have important figures in their tribes called Shayks. Shayks are essentially "first among equals". They are deferred to for wise information when a good mediator is needed. Shayks or Shaykhs (or sheikhs in modern Arabic) have been mistakenly called "Sheiks" in movies, but that is not the case because if it is not spelled with kh, it would be pronounced like "chic".
Mecca became most important for trade because it was an Oasis, a place to pilgrimage for worship of early pagan deities. The shrine in Mecca where the gods reside is called the Ka'aba. The most important tribe was the one that controlled and took care of the shrine. Called the Quaraysh, they basically controlled the security of Mecca They settled there around the year 300. Not all Quaraysh settled in Mecca, some remained nomads. Mecca was a place where all tribe fights were put aside. The Quaraysh maintained that peace for the sake of trade and religious purposes.
The emergence if Islam was especially radical to the Bedouins because it stressed that the number one alliance should be with god, whereas Bedouins always had their number one alliance with their tribe. After Islamic conquests, they began to migrate to North Africa, with their other main areas of occupation being Syria and Egypt. Currently Bedouins make up 10% of the population of the Middle East. More and more of them become settled or semi-settled as time goes on due to the difficulty of the weather and the ease of modern societies. Also, the switch between camels and trucks cut down the need for seasonal migrations. Depending on the country, many families essentially have two lives, part in settlements and part in the desert or with herds. (Settlement isn't entirely by choice, it depends on the country. Closed borders can keep them from migrating to tribal territories and/or grazing lands, as well the limitations of harsh weather in the deserts.)
Sources:
http://i-cias.com/e.o/bedouins.htm
Lecture from UCF Dr. Stockdale in ASH3222 "Islam and Empires"
Some information given by heyoka (thank you)