Anthropology is a social science which can be defined, most broadly, as the study of humankind. Put this way, it is clear that philosophers have been concerned with anthropology since ancient times, for example when they theorized about what it means to be human. Anthropology as we know it today began to emerge as a science in the mid-nineteenth century, and was from these beginnings linked to other emergent sciences such as biology, geology, psychology, and linguistics. What sets anthropology apart from these and other sciences is the concept of culture, which Edward Tylor defined in 1871 as "that complex whole which includes knowledge, belief, art, law, morals, custom and any other capabilities and habits acquired by man (sic) as a member of society". Today anthropologists tend to define culture as an integrated system of values, beliefs, and norms of conduct which are acquired socially and which delimit the range of acceptable behaviours for a particular social group.
This broad field of study is broken down into several subdisciplines, which I will speak from a North American perspective, since that is where I studied the discipline.
Physical anthropology or biological anthropology is concerned with humans as biological organisms, and includes paleontology, specifically the study of fossil remains of ancient humans and their predecessors; primatology, the study of primates, our closest living relatives; and the study of modern human variation. Louis Leakey and his son Richard Leakey are famous physical anthropologists who found many early hominid remains and helped to piece together a picture of humans evolving from primitive ancestors into modern Homo sapiens. Jane Goodall, Dian Fossey, and Birute Galdikas are all well-known primatologists who have devoted their lives to studying the social lives of primates - chimpanzees, gorillas, and orangutans, respectively (and all, interestingly, were recruited to do so by Louis Leakey). Physical anthropologists who study modern human variation are not famous or romantic figures like the others, but they are interested in the ways in which modern humans vary in terms of, for example, blood type, skin colour, or genotype. What unifies these threads of physical anthropology is the emphasis on how and why humans evolved into the biologically diverse populations we find in the world today.
In contrast to the biological perspective of physical anthropology, the other branches are cultural in orientation.
Archaeology or archeology is the study of the cultural past through the material remains that past people left behind when they died. The popular image of the archaeologist is the toiler in Egypt, uncovering lost tombs full of riches, but not all archaeologists focus on such monumental or ancient sites. Archaeologist might be involved in the excavation of middens left by First Nations groups a few hundred years ago, or the uncovering of shards of pottery made by prehistoric people thousands of years ago. Archaeology is not, I am told, as romantic as it sounds, and archaeological fieldwork generally consists of days and weeks spent on hands and knees painstakingly uncovering tiny bits of unidentifiable chips with toothbrushes, but if you have the inclination and the money you can take part in digs around the world. Do an internet search on archaeological fieldwork to turn up lots of opportunities.
Linguistic anthropology deals with the complex systems of symbols which constitute human language. Descriptive linguistics studies how languages are constructed. Historical linguistics studies how languages grow and change. Sociolinguistics is concerned with the relationship between language and social divisions like gender, age, and class. Although linguistic anthropology is a branch of anthropology unto itself, most cultural anthropologists are interested in the relationship between language and culture; have a look at the Sapir-Whorf hypothesis for more on this.
Cultural, social, or sociocultural anthropology is the study of the social, symbolic and material lives of contemporary and recent historical human societies. Unlike archaeologists, who must study cultures second hand, sociocultural anthropologists research them directly. Ideally, sociocultural anthropologists do ethnography or fieldwork as part of their study. This involves going to live with the people under study; the stereotypical romantic vision is of a white man in a pith helmet and stout boots, setting off to live in a thatched hut for a year or two, and this was indeed what the pioneer of this methodology, Bronislaw Malinowski, did. But early social anthropologists included women like Margaret Mead and Ruth Benedict, and today sociocultural anthropologists often do fieldwork in urban environments or their own home communities, studying a particular subculture, perhaps. In the field, sociocultural anthropologists engage in participant observation, an oxymoron which captures in its contradictory terminology a tension at the heart of ethnographic methodology: the ethnographer is participating in a community, learning the language, eating with the people, taking part in their rituals and customs, yet is at the same time outside the group, observing people, writing notes about them, analyzing them. Back home, the ethnographer churns out a tome called an ethnography, and out of these ethnographies grows the broader and more generalized study of ethnology, the analysis and comparison of different cultures.
Anthropology might be a bullshit science, but I don't think so. Anthropology teaches us to avoid ethnocentrism and to respect the diversity of human life through history and across cultures. In this age of global travel and mass tourism, fewer idiots abroad can only be a good thing.