Reimaging
Reimaging is the process of removing all software on a hard drive, wiping it clean and then reinstalling everything. All of this is done in one process and you don't loose any data.
A reimage becomes necessary if your operating system becomes damaged or corrupted. You may also need to reimage if your system is plagued with spyware problems.
This process is different from placing your recovery disk in the drive and reinstalling your OS, as reimaging covers all the software on your machine and not only your OS. It is like a fresh install of your complete hard drive.
Reinstalling
Reinstalling is the process whereby the hard drive is reformatted (wiped clean) and all the software reinstalled, including the Operating System (OS). This is a very time consuming task and it's success depends on you having copies of all the software present on your machine at the time of reinstallation, or at least the applications that you want to reinstall. You will loose all personalised data and configurations.