A slipper clutch is simply a mechanical device that, when activated, automatically separates the clutch plates. When you downshift the engine's revs increase due to lower gear. At this point, because the engine isn't under power, the rear wheel attempts to turn the engine, which can be a bad thing and is called back-torque.
Under power the engine has a rev limiter to stop it getting over revved and in turn damaging its internals. However, when the rear wheel is turning the engine there is no rev limiter – which is where the slipper clutch comes in.
Inside a slipper clutch is a center piece that lifts up on a series of ramps. These ramps lock in one direction (when the engine is turning the rear wheel) but not in the other and so when the back-torque is too much the clutch's center piece lifts and releases some of the pressure on the clutch plates – effectively pulling the clutch lever.
When the pressure reduces the center piece drop down, reengaging the clutch at a set rate until the back-torque is once again too high. On track, a slipper clutch is a wise investment.