since repairing permissions is explained elsewhere and can be found easily enough with a search or looking at the stickies....
a beachball is one of two things, both mentioned already...
1. a beach toy that is inflatable and round and multicolored
2. when your Mac is 'busy' with an application and your mouse changes to a spinning multicolored ball that resembles a beachball. this only happens when a app is locked up momentarily or is having an issue it cannot resolve. usually more ram or force quitting the app helps