So I'm going to assume you are talking about your truck or motorhome. The Regen is the process that burns off the diesel particulates (black smoke) that is caught in a filter. It burns it off and cleans the filter.
As for the exhaust brake- This is a system that uses your engine to help brake your vehicle so you don't burn up your brakes trying to stop. This is very helpful and is great to use while driving down steep grades. I use it all the time while towing. Helps to take some wear off of the brakes.