The Chicago style is a set of citation rules created by the University of Chicago Press. This style is widely used in publishing, and is also used by other humanities and social sciences disciplines. For some examples, see the citation guide from The Chicago Manual of Style Online as well as the Chicago Style section of Purdue University's Online Writing Lab (OWL).
Unlike the APA and MLA, The Chicago Manual of Style provides two alternative formats: the (1) Notes and Bibliography format and (2) the Author-Date format. Consult with your instructor to determine which of the systems you should use.
If you've written in other formats, one of the first things you may notice about CMOS is how much more complicated it is. There are a lot more options, and far fewer clear-cut rules. "Why then," you might ask, "would anyone use this format?"
It helps to know that Chicago Style was originally created for Humanities scholars. Though several Humanities fields occasionally allow other styles for students, in most colleges and universities History departments tend to retain the requirement to use CMOS.
Beyond this, if you end up doing any professional writing and/or proofreading after you graduate, you'll likely find that CMOS is the style of choice. (As you would expect, this is especially true if you're writing in any of the traditional Humanities fields.)