REGEN is the burning of soot built up in a DPF.
The Emissions Equipment for diesel trucks has changed quite a bit through out the years. In 2004.5 all heavy duty diesel pickups had to install EGR's which is the exhaust gas recirculation system. Basically it turns exhaust into inert gas and directs the gas back into the combustion process. Then in 2007.5 the EPA required pickups to use a DPF. The DPF, or Diesel Particulate Filter, is a filter that catches soot, or unburnt fuel from the exhaust. Once the soot builds up, the exhaust heats up to burn the soot off. Starting in 2011 Diesel Exhaust Fluid is used to treat NOx emissions, in addition to the EGR and DPF treating the carbon emissions.
The DPF is a crucile part of treating diesel emissions and each OEM utilizes and operates their DPF a little differently. Below, the DPF in the 2011-2016 LML Duramax is explained.
CHECK OUT THESE OTHER LINKS ABOUT REGEN AND DPF's