The Chicago Manual of Style is a set of guidelines for documenting sources and formatting papers. Author-date is one system used in the Chicago Style. The other style used is the Notes-bibliography system, using footnotes. Please verify with your professor which system you are to use. The Author-date system is commonly used and is similar to both MLA and APA in format.
Reasons to use a citation format:
Giving credit to the authors and avoiding plagiarism
Show readers where you incorporated research and evidence
Unify the presentation of the information and convey professional communication skills