This is such a can of worms...and it has two sides to the story.
First, I used to be an English teacher at the high school level (until I realized my 2 week paycheque was enough to cover about 6 days). There is a real concern with plagiarism, not just as a punishment measure for lazy or over-ambitious students, but because there are an alarming number of kids getting through the system who are functionally illiterate. (They write for Dirt Bike magazine...and vote Democrat)
IF a good teacher has enough time to get to know a kid's writing, it becomes obvious when plagiarism occurs. A sudden change in cadence, sophisticated vocabulary, or citing cultural references out of his/her demographic (ie. a 13 year old who sprinkles a lesser-known quote from Mahatma Ghandi might raise an eyebrow) are cues. It's not that different from a musician who winces when someone plays a guitar that's even marginally out of tune...when most folks don't notice the difference. You develop a sensibility for detecting these things. I taught 150 kids a year, but if I found a naughty note on the floor, I could tell by the handwriting and a couple of misspelled words who authored it.
That said, lazy writer also have lazy sources, and a good teacher becomes familiar with the reference books in the school library, the Coles Notes for class novels, and popular file sharing and websites from the internet or Microsoft Encarta. That's outright plagiarism, not subtle, and easy to catch. Of course, those students tend to be confrontational knuckleheads and want to play lawyer when they get caught, so they burn up a lot of time we could use...ummm....teaching...
The plagiarism sites that are out there, to me, are like DNA testing. You're going to get partial matches for phrases because we learn to write by reading and listening, and one tends to follow a pattern. For instance, if I told you to use the word "furtively" in a sentence, 90% of people would write the word "glanced" in front of it. ie. "John glanced furtively around the room." It's an underused word that we only hear delivered in a predictable way. In a given essay, especially when one develops a certain ease with writing, you're going to find expressions, colloquialisms, adages, stylistic borrowings, and a discomfort with tougher vocabulary that forces the student to produce very predictable sentences. That's all part of the discovery process, something one works through to become a flexible, fluid writer. Unfortunately, if you run that essay through a plagiarism checker, it's going to light up like a (you guessed it) Christmas tree (see, you knew I'd say that, right!)
Back to my DNA thing; if your teacher calls you to the carpet over potential plagiarism, it's probably just because the sum of all these little common expressions and partial sentences added up to a potential problem. Unless you're at the Master's degree level, referencing and quotations are difficult to execute without "accidental" borrowing. What the teacher is really looking for is an essay that is either entirely stolen or a hodge-podge of 3 or 4 major sources jammed together. That's a "DNA Match." You're busted. Go to jail. 30 kickstarts of a drowned WR426. However, a person clever enough to bring 5 or 6 lesser-known reference works together in a writing style that is even close to being consistent throughout is a person who is clever enough to write without plagiarizing. It would take less work to be original.
All your teacher wants to know is if you're an illiterate hiding behind borrowed work (and many illiterate people are highly intelligent and can fool very experienced teachers), or a decent student who is being lazy and dishonest. Flip the coin for a second. A teacher who uses a plagiarism program as the sole means of detecting borrowed or stolen work is also lazy and hiding behind an imperfect tool. If the essay turns out to be 93% "plagiarized," but no one paragraph is attributable to a source, all you're guilty of is using average sentences in an average way. Bottom line: the plagiarism program is just one more tool in a teacher's quest to evaluate the true talent and writing level of his/her student. If you're feeling like it's a "guilty until proven innocent" accusation, you need to have a heartfelt discussion with your teacher. If you do nothing, you'll lose. If you get in a confrontation, you'll lose. If you are genuine and patient, you'll win.
Go win.