From what I can tell, access to be able to push content to the Chumby from their web site. They allow you to configure "Channels" that are basically playlists of flash apps that cycle on the display of the device. So a morning channel could be a weather app, some news app, and maybe a traffic app. If the unit doesn't have the flash app you configure on the site, the Chumby pulls it down off their servers.
The ads they inject end up being a quick little flash ad with no sound that come between your channels. I've only seen one so far, and it was a Chumby 101 info ad.
The device does let you freeze one app on the screen instead of auto cycling. I'm not sure if doing so stops the ads as well. I'd assume so, as I had an app frozen for over 24 hours along with a partial screen overwrite from my hacks, and it was never cleared off.