Plagiarism is using someone else's work without crediting the original author or creator. This includes the use of any ideas, research, or analysis of a topic, that were written by someone else, even if you have not used their exact words.
Obvious examples of plagiarism are copying and pasting parts of an article or online encylopedia essay into your own paper. However, even the accidental omission of a citation for a source is regarded as plagiarism.
No one has ever failed a class for using too many citations, however you could fail a class, or even be expelled, for failing to cite the sources you have used.
For more information on these concepts, see the guide Ethical Use of Information.