01. 'What are permissions in OS X?' - Well, first - welcome to the wacky world of UNIX; and, see here
02. '... what would be the benefit of repairing them' - Well, MacOS X (10.0.0 - 10.4.2) itself, at times likes to change the permissions of files (for unknown reasons); plus, you may have created or received a (document or application) file or files, and / or folders - whose permission(s) settings are not correct.
Then there are those times when you either re-install your MacOS X altogether, and / or install a related 'Update', 'ComboUpdate', or 'SecurityUpdate', etc. package. Prior to performing such an installation, it is now a common ritual to launch 'Disk Utility' and select 'Disk Repair', followed by selecting 'Repair Disk Permissions'. Then, once the new installation is completed - you are to once again launch 'Disk Utility' and select 'Repair Disk Permissions'.
Failure to perform such steps can result in an application not launching, etc.
Unlike with System 9.2.2 and earlier - where 'routine maintenance' was practically non-existent; with MacOS X it is now a monthly, weekly, or even (for some) a daily necessity!
Should you want the very OS that changes your permissions - to eh, fix those improperly changed permission settings - as well as, the permission settings of other files and / or folders, then consider this process
I know, I know; and, you thought you purchased a Mac.