What is APA?
APA stands for the American Psychological Association. According to the APA website, "APA is the leading scientific and professional organization representing psychology in the United States, with more than 115,700 researchers, educators, clinicians, consultants and students as its members" (http://www.apa.org/about/index.aspx).
APA style is a method of documenting resources in academic writing within scientific writing, which includes the fields of all sciences, including social sciences such as psychology, sociology, education, and criminal justice. As with MLA, "APA style consists of rules or guidelines that a publisher observes to ensure clear and consistent presentation of written material" (http://www.apastyle.org). Using APA style applies to not only how you write, but also how you cite and how you format your paper.
This question applies to any citation style. Why do we need citations?
When asked why you should cite your sources, many students reply, "So you don't get accused of plagiarizing." It is true that you must provide citations crediting others' work so as to avoid plagiarism, but scholars use citations for many reasons:
To make your arguments more credible. You want to use the very best evidence to support your claims. For example, if you are citing a statistic about a disease, you should use a reputable source like the World Health Organization or Centers for Disease Control (CDC). When you tell your reader the statistic comes from such a source, she will know to trust it- and thereby trust your argument more.
To show you've done your homework. You want to make it clear to your audience that you've researched your subject and know what you are talking about. As you dive deeper into your research, you will probably find certain authors are experts on the topic and are mentioned in most of the articles and books. You should read these experts' works and incorporate them into your paper.
To build a foundation for your paper. Great breakthroughs in scholarship are accomplished by building on the earlier, groundbreaking work of others. For example, Isaac Newton's law of universal gravitation would not have been possible without Johannes Kepler's law of planetary motion. What articles, books, texts, etc inspired you to create your argument? You want to provide references to the works which led to your thesis.
To allow your readers to find the sources for themselves. Someone interested in your topic may be inspired to read some of the articles and other sources you used to write your paper. The citation within the paper tells them what part of your argument is best addressed by a particular source, and the full citation in the bibliography provides them with the information needed to locate the original work.
(This information has been politely borrowed from Radford University's McConnell Library)