Parallels creates a virtual machine. It allows you to run Windows on virtual hardware instead of the actual hardware. It means you run Windows on top of OS X. So you can access both the Windows programs and the Mac programs at the same time, even copy and paste between them. Rather than splitting off a piece of your hard drive, Windows and everything in it is sitting on one big giant file. If you want to get rid of Windows, you just erase the file. The advantage of this is convenience- you can boot up Windows easily and just do a couple things, then switch back to your Mac stuff. The disadvantage is performance. Because it's running on virtual hardware, it's not going to be as good as if it was running on your actual hardware. The new version of Parallels has DirectX 9.0c support so you can play games on it, but I wouldn't recommend playing anything intensive because your frame-rate would get pretty low.
Boot Camp isn't actually a program. It's the tools you use to dual-boot your computer. There's three pieces to it. The first is the Boot Camp Assistant, which partitions your hard drive to make room for Windows. The second is a compatibility layer in the firmware (you don't see this) because Windows uses the older BIOS to boot while Macs use EFI. The third part is a set of drivers for the Apple hardware, which comes on your OS X install disk. When you run this, your computer becomes an Apple-branded Windows machine. It's exactly the same as any other Windows machine running that hardware in terms of capabilities and performance. You can switch back and forth between Windows and OS X, but you must restart the computer to do so.
