Anthropology "speaks" to us because, as one of the eNotes documents attached below notes, "it is the study of humanity." Or, as the American Anthropological Association defines it, it is "the study of humans, past and present...anthropology draws and builds upon knowledge from the social and biological sciences as well as the humanities and physical sciences. A central concern of anthropologists is the application of knowledge to the solution of human problems." [www.aaanet.org/about/whatisanthropology.cfm]
The world is composed of hundreds of ethnicities, languages and cultures. Understanding how humans of myriad ethnicities, cultures and languages interact and how they have evolved over the centuries is crucial to the advancement of the species. If, as George Santayana postulated, those who ignore history are condemned to repeat it, then it follows logically that those who ignore the origins and development of humanity are destined to repeat the mistakes of those who came before us. Insomuch as the study of anthropology includes both archealogical and sociocultural components, then the higher the level of knowledge of what caused earlier civilizations to perish the greater the prospects that contemporary man can avoid the same traps. Anthropology, then, is the key to understanding where we came from, and where we may be headed. In that, it speaks to all mankind.
Anthropology is the study of humankind—a very broad definition, so I like to give an example of what anthropology is, and how it speaks to us, by reading from a New York Times article about a man from Kenya who uses witchcraft to influence the outcome of soccer games. When I read the article to my students it sounds, at first, kind of funny or strange that a person throwing seashells on a table as a way to analyze the pattern of the future without his intervention, and one who uses a secret green powder rubbed into his palms to help him with the exercise, really thinks that this "juju" works. However, when we consider this "juju" within the larger context of our own superstitions, e.g., athletes who don't cut their hair for good luck (or those who don't change their underwear), or throwing salt over our shoulders, or never walking under ladders, or knocking on wood, it makes much more sense and brings us to a better understanding of "our humanity".
So, when we begin to look at other cultures, i.e., study humankind through an anthropological lens, and begin to think about what makes us different, what makes us similar, and why, this is what anthropology is all about and how it speaks to us. Clifford Geertz says it even better: "The aim of anthropology is to enlarge the universe of human discourse."