Regen is a "feature" of most modern FEL (Front End Loader) valves, it's on the Dump (joystick far right) circuit, and is also referred to as "Fast Dump". The reason it is nice to have is that without it, the weight of a filled bucket can actually "pull" the bucket down faster then the fluid can enter the other side of the cylinder, this will create a air pocket and give the bucket a "floppy" feeling until the joystick is held in the dump mode a few seconds to refill the cylinder pushing the air past the seals. So we add "regen" or "regenerative" function to the valve.
Regen solves this problem by actually filling both sides of the cylinder at the same time with hydraulic fluid. But how will that work you might ask? Well, because there is more volume on the side of the cylinder that extends it since the rod is taking up space in the other side, it "overpowers" the rod side and lets the cylinder extend-thereby dumping the bucket. So since now both sides of the cylinder are "pressurized", the air pocket can not develop, eliminating the "floppy" bucket syndrome. One other added bonus is that the bucket actually dumps faster due to the higher flow rate required to do all this, that's why it's referred to as "fast dump" sometimes.
So, now you may be asking “This is cool and all that, but why do I need to know about it?” The answer to that is simple, if you ever try to run a snow plow with two SA (single acting) cylinders, or a cylinder that drives a chute rotator on a snowblower you will soon find out that they won’t work if you push the joystick to far right into the regen mode. The plow won’t work because since both lines are pressurized-both cylinders will be trying to extend at the same time binding everything up. The rotator won’t work because there is no weight pushing the cylinder closed like there is on the loader.
On most, if not all John Deere tractors there is a “lockout” the limits how far the joystick travels to the right to keep it out of the regen mode.