What is a citation?
Webster's Dictionary defines "citation" as the act of citing a passage from a book, or from another person, in his own words; also, the passage or words quoted; quotation.
What is a bibliography?
The American Heritage Dictionary defines "bibliography" as a list of writings used or considered by an author in preparing a particular work.
How are they different?
Often times, we used citation and bibliography to mean the same thing. Sometimes, we also use the terms "reference list" or "works cited." However, technically, a citation is used for something you quote from and a bibliography is a list of every source you use to write your paper -- whether you quote from it or not.
Why should I cite?
Well, mainly, because your professor expects you to. That said, citing your sources also shows that you have done research using authoritative sources. Also, bibliographies act as further reading lists and help guide the reader of your paper to additional sources on that particular topic.
For more information on citing in different styles, please refer to the citation guide.