On any *nix OS, like Mac OS X, every application, file and folder has an owner and a permission. This determines who has the right to read, execute or write to those files, and this is an important security feature in these OSs. Unless you have root/administrator privileges, you cannot touch any files/folders that doesn't belong to you unless the owner of the files (which may be the system itself) permits this.
Every now and then - often by dodgy 3rd party installers, but most recently by the iTunes 7 installer - these ownerships and/or permissions of some files and folders gets messed up, and this might cause programs to misbehave (refuse to start, work slowly, miss features, etc). By repairing the permissions you reset these to what they should be (according to your system).