In the short answer, SVN (Subversion) is a code control system that was built on CVS (Concurrent Versions System)
Basically... you write a bunch of code/program/library whatever, check this into a CVS(or SVN) system and call it version 1.
Then.. when you work on this project more you check-out and check-in files. The software or CVS/SVN system then takes care of file version info ie. version 220.127.116.11.001 etc and will do all kinds of cool things like show you the changes made between two file versions (diffs).
There is a ton of functionality and a lot more to it, and is handy if you have a decent size project and/or multiple developers working on the same code. (as you are warned about versions etc)