In a nutshell, Parallels is a program that runs within OS X. You can then run Windows inside of Parallels. The benefit is that you get to run Windows and OS X apps simultaneously. The trade off is sharing resources between two operating systems - thereby slowing both down.
Boot Camp is special software that partitions (splits) your hard drive into two or more virtual pieces -- one for OS X, and others for Windows, Linux, etc. You'll then have a choice, when you start your Mac, to choose which operating system you want to use. The benefit is that, whether you're using OS X or Windows or Linux, you'll have all the system resources available. The trade off is that it's slower to shut down OSX, and reboot into Windows (and the reverse) than it would be to start a Parallels session.
Hope this helps!
J
PS... A word to the wise: folks around here refer to Macintosh computers as either Mac or mac - but never MAC.