Plagiarism is the use of another person's words or ideas with the goal of deceiving readers into thinking the plagiarist originated the ideas and deserves credit for them. It is considered a very serious offense in the academic world, and students, professors and even college presidents are regularly punished for it.
Colleges have elaborate rules on how students can avoid plagiarism by quotations and citations. Note that when academic credit for original writing is not at issue, plagiarism does not happen. Thus officials of government or the private sector often give speeches or reports, and take credit for them, even though some staff member actually did the research and writing. That is not plagiarism because no academic credit is claimed, plus the speech writers are paid for their services.
|“||Plagiarism is passing off a source’s information, ideas, or words as your own by omitting to acknowledge that source—an act of lying, cheating, and stealing.||”|
See also Harvard's "Writing with Sources: Common Questions about Sources" (emphasis added):
4. Am I plagiarizing if I accidentally use a few vivid phrases from my reading without citing them? Yes; it’s your responsibility to avoid such accidents (p. 14b).}}
Relation to copyright
Plagiarism and copyright infringement are separate concepts, and don't necessarily overlap. An act of plagiarism can also qualify as copyright infringement if the work being copied is copyrighted. However, it is still plagiarism to copy a work that is in the public domain without providing a citation.
Science fiction author Harlan Ellison sued and won in a case against James Cameron, claiming that his film The Terminator plagiarized the two episodes he wrote for the television show The Outer Limits: "Soldier" and "Demon with a Glass Hand".  The case was settled out of court, with Ellison gaining a spot in the film's credits.
Plagiarism and the Internet
Plagiarism is an ever-increasing problem in schools. With the widespread popularity of the Internet, it has become much easier for students to directly plagiarize information; rather than laboriously copying it from a book, they can now simply cut-and-paste electronically. The problem is exacerbated by the existence of online sites offering pre-written papers for a fee. 
Associated Press reported: "On the plagiarism issue, Biden correctly attributed lines in one of his speeches to former British Labor Party leader Neil Kinnock on some occasions, but not at an Iowa State Fair debate where Biden was videotaped. In political campaigns, no black mark is too old to dredge up — again. Biden admitted back in 1987 that he had committed plagiarism while a freshman at Syracuse University law school and that he occasionally used other people's words in his speeches without giving credit. 
- NewsBusters - Dave Pierre