It's more of a ritualised tradition now but it looks like a huge amount of fun and I'm intending to go to atleast one common riding this spring/summer.
Basically you get several hundred really well turned out horses and there's one leader with a flag and you set off on a few hour long trail ride with a lot of galloping etc. there are also a lot of watchers and there's usually other things going on too like scottish dancing etc.
Here's a video clip I found taken on one of the Common Ridings last year
Look at all those riders!
I live in Edinburgh and only started riding here last November so wasn't really aware of that tradition. I'm just taking lessons every week now, the stable I take lessons at leases horses for the common ridings so I'll arrange it with them. Should be a huge amount of fun although I guess I sort of need to buy a riding jacket. Don't have one now.