Named after Kate L. Turabian, the late graduate school dissertation secretary of University of Chicago, the style nowadays is "essentially the same as those presented in The Chicago Manual of Style, 15th edition, with slight modifications for the needs of student writers" (Turabian). Sounds nice, no?
Upon first inspection, I could see several similarities between Turabian and MLA and APA, and for good reason. Turabian is divided into two sub-styles: notes-bibliography style for the literature and history kids, and parenthetical citations-reference list style for the science folk. Take a look at this example on the official online Turabian Citation Guide:
One authorThe parenthetical in particular reminds me of the MLA and APA style both in that it includes a year following the author's name, but it doesn't have a "p." before the page number to denote that it is the page number. APA style is seen in the reference in terms of the method in which the title of the work is capitalized.
Note: 1. Wendy Doniger, Splitting the Difference (Chicago: University of Chicago Press, 1999), 65.
Bibliographic: Doniger, Wendy. Splitting the Difference. Chicago: University of Chicago Press, 1999.
Parenthetical: (Doniger 1999, 65)
Reference: Doniger, Wendy. 1999. Splitting the difference. Chicago: University of Chicago Press.
Turabian is a curious style in that it covers nearly the entire spectrum of academic research. Your safest bet is to always go with the style your instructor suggests or requires, but should you find yourself in a class with a bit more leniency given to your chosen citation style, I suggest giving Turabian a try. Regardless of where you're coming from academically, you'll find that the transition to Turabian should be relatively painless.