okay, here's the best method of explanation i can give you...
Any file or folder in OS X has permissions dictating which users can read, write, or run (execute) a program/file.
Many of the system files will become so altered that you (your username) cannot read, write or execute things that you need need to... For instance, iTunes might try to read it's song lists on starting, and find them locked to your username (iTunes will run as a process owned by you, so it is governed by the same rules that you are).
Repairing permissions checks and resets the permissions on all of the system files (and i think programs made by apple). It won't do every file, just system ones, which is why you can only repair permissions on disks that have OS X installed on them...
Then, when it's finished, you and your programs will have proper clearance within the system to access specific files.
hope that helps??
pnw