Subversion (or SVN for short) is a versioning system. All the code is placed on one server (the repository). Every change is stored. You can always "roll back" to a previous version. You can also have multiple versions of the code, i.e.: when you have a release candidate 1 (RC 1) of your software, and you deliver it to the client, other people can start working on the next bleeding-edge version.
It's really handy to read (a part of) the Subversion Book. It's handy when you want to talk about things like tags, branches, committing, updating and other buzzwords.
Roderik: Always create a backup of the SVN repository as a SVN user. If you do it as root, other users will get in trouble with file permissions.