Meta lesson: What are permissions?
Permissions determine who has access to a file and to what degree.
When you verify permissions, you are checking Apple installed files (generally the base system) against the package receipts to ensure that the permissions on the file or folder match what Apple intended.
A repair corrects any issues found during the verify. For example, it would be bad if certain files could not be read by the OS because of permissions, so this process would correct that.
This is not something you should do unless you are having a permissions related problem with a system file. There are a few reasons:
1. The permissions "database" at times isnt not updated. For example, let's say Apple has changed the permissions on Directory Utility in 10.6.7 but your package receipts are from 10.6.3. You will likely get error messages, but nothing will change. In fact, Apple has a huge KB documenting permission messages you can ignore.
http://support.apple.com/kb/ts1448
The information only serves to freak people out. If you have a permission issue, you will know.
2. Because of number 1, you could in theory break things by attempting to use this as a form of maintenance.
3. Using it as a form of maintenance is a myth perpetuated by folks who dont know what they are doing and some issue magically cleared up this one time they did a repair.
To close, don't worry about it. Most permission related issues people have aren't even in the scope of Disk Utility's repair permissions funtion.
