Here are the main differences.

Temporary - a redirect you only wish to have for a temporary amount of time.
Permanent - a redirect you wish to keep forever.

This tutorial should also help:

http://wiki.lunarpages.com/Redirect_Pages_in_cPanel

A temporary (302) redirect tells the other party (search engine, browser, etc.) to temporarily use this new address, but that the old one is expected to return at some time.

A permanent (301) redirect tells the other party to replace the old address with the new one, and to forget about the old one, as you'll never see it again.

When a search engine sees a 302, it will retain the old address, because it's expected to be in use again. When it sees a 301, it updates its records with the new address. Both 301 and 302 return a new address (URL) to be used and displayed, but in one case it's just temporary and in the other it's a permanent change. Think of the Post Office forwarding your mail -- it can be for a limited time, or you move and it's permanent.