A citation is a way to tell your readers where you found your sources, and it also gives your readers enough information (such as author, title, page numbers, etc.) to find the sources themselves. A citation can be in-text (when the author's name is part of a sentence) or parenthetical (when the author's name and the page number appear in parentheses). Many citations are both, with some of the information placed in the sentence and some in parentheses.
A citation style is a set of rules that tells you how to format your citations and what information you have to include. It is a standardized documentation format set and regulated by a specific organization. Citation styles are used not only in formal publishing, but also in colleges and universities.
A bibliography is a list of works (books, articles, etc.) that can be used for background or further reading. Sometimes these lists contain descriptive notes, which add details to the list. If this is the case, then the list is referred to as an annotated bibliography.
When you do research, you work with other people's ideas as well as your own. This is an integral part of research, to combine your ideas with the ideas of others and create something new. It is very important that you give credit where credit is due, and this is one reason you need to cite your sources. If you don't, you're committing plagiarism, which is is both lying and stealing. When you cite your sources, you tell your readers about where you found some of the inspiration for your work, and you credit those who inspired you, or those whose work you used. Also, when you cite your sources, you help your readers find those sources if they wish to read more about the ideas presented in your work.
Whenever you use information from articles, books, interviews, etc., you must credit the authors of those works by citing the sources. When the information you're using is your own idea, or when the information is common knowledge (for example, that Thomas Jefferson was president of the United States), then you do not need to cite.
Rewording something is called "paraphrasing." If you paraphrase, you still have to cite your source, because the ideas you are using belong to another person.
