I subtley agitate my carboy during secondary for two main reasons....kinda like an off-centered spinning top.
1. If my gravity seemed a bit high after primary and had been in primary for longer than 10 days, I hope to re-suspend some of the yeast so that it can dry out a bit and 'clean-up' or 'condition' the beer a bit more.
2. When x-ferring the beer from primary to secondary you end up with a bit of headspace in the carboy. By agitating the carboy ever so slightly you create a blanket of CO2 into the headspace....helping to protect your beer from oxidation.
I'd be really interested to hear why other people agitate their secondary.
Conical: gobs of sanitizer
Primary: O-Town Cider, German Pils Do-over
On Draft: All-Calypso APA, German Pilsener, Coffee-Cocoa Nib Stout, American Amber Ale
On-Deck: Imperial Chai Tea Brown Ale, Big Bock B*tch, something funky and belgian