You plagiarize when you take someone's ideas or words and pass them off as your own. It's a fancy word for copying. Many politicians and writers have plagiarized. It's not always professional suicide, however — just ask Vice President Joe Biden. Still, don't do it.
It's not illegal to plagiarize but it's morally wrong, and it might just get you tossed out of school. If you're writing something and include word-for-word something you've read and don't attribute the words or ideas to that writer, you are plagiarizing. The origins of the word are said to mean "one who kidnaps the child of another" — which certainly gives a sense of the gravity of the charge. After all, some writers do consider their words to be their babies.