What is APA?
APA stands for American Psychological Association, which is the professional body of psychologists who created this citation style. When you write a paper, you usually have to use and then write about other people's research. When you refer to someone else's work in your paper, or quote it directly, you need to say where you got it from (aka "cite your source"). The way you cite your source depends on the citation style you are using. A citation style is a set of rules for how you cite other people's work in your paper.
You need to cite your source in two places: a short version in the paper, right after your quote (this is called the 'in-text citation) which leads the reader to the full version with all of the information about the author, date etc etc, at the end of the paper (in the list of references at the end, known as the "References").
The APA created a set of rules for psychology researchers a long time ago, and now it is the most popular citation style in the social sciences. There are others (MLA, Chicago, Turabian, etc) but it's best to stick with the one that is standard for your field (and of course, always use the one your instructor has asked you to use).
To see simple example of references created in APA style, see the Basics link below. For more information about in-text citations as well as reference lists, click on the APA Citation Guide and the Purdue OWL Guide links below.