Art history is all about the art of the past - looking at it, finding out about it and experiencing it (and no, its not always about dead guys). Pretty straightforward really, so the next question is, why bother?
Well, for one thing, art connects us to the past as it binds us to one another even more in the present... unifying us in a world of cultural diversity. Not only that, art in any form -- painting, sculpture, architecture -- acts as a guardian of our culture.
Works of art present a record of the thoughts, feelings and efforts of groups of people throughout history. Think about it... how would we possibly know our collective visual history... the rulers of our lands ... the landscapes of long ago times or the faces of our ancestors, if not for art history?