I used to teach a course on this at a community college in the English Dept. "Plagarism" is not complicated or hard to understand. Plagarism is lifting verbatim, word for word, stuff somebody else wrote and pretending it is your own work. Common instances are copying word for word encyclopedia entries, copying, word for word--exactly as it was written--from a book, an article, a website, a screenplay, song lyrics, or any other written piece of material, and putting your name on it and saying or implying you yourself wrote it.
The reason this is bad is because you are stealing somebody else's original stuff. It is also illegal and can cost you. And it can really cost you big time if you happen to make money by copying word for word somebody else's writing and put it out there in the marketplace, claiming you wrote it yourself. That's what the copyright laws are all about. And the U.S. courts are very strict in enforcing the copyright laws. They especially like to nail people who plagarized for commercial gain.
The gray areas where the courts have a lot of latitude and disgression are in imitation of plots, characters and other vague aspects about a written work which are strikingly similar to someone else's previously copyrighted work.
The whole point of copyrighting a book, song, screenplay, etc. is to protect what you labored over and created as an original written work, and to prevent someone from stealing it from you. You see, the legal system and the courts recognize your hard work and are there to protect you from getting ripped off. That's why Congress enacted copyright laws in the first place.
Some things not protected by copyright law are un-copyrighted works, book, movie, song, etc. titles, informal discussions with a publisher about a book idea you have and the like.
Most of today's students don't understand why they can't do their term papers by copying and pasting stuff into their work from the web. They figure, it's out there, nobody's watching, what's the big deal?
Well, I've found that it's impossible to change this attitude in some students. That's why such sites as turnitin.com and copyscape.com exit. If you steal somebody else's words, you're a thief, and that's it. And these sites will catch you.