IMAP is a protocol for accessing email - an alternative to POP. It is considered better than POP for those who need to access their mail from multiple computers. This
writeup at The IMAP Connection explains it better than I could.
The one drawback to GMail is that it is POP-only. That's one of the reasons for all the troubles people have had setting it up to work nicely on the iPhone (downloading a bunch of old mail, etc.). If/when Google enables IMAP on GMail it will be pretty much perfect.