Shadow Plus was first introduced in 2012 with the Shimano XTR rear derailleur. It prevents chain slap and keeps the drivetrain quiet. It also reduces the risk of a chain jumping off.
This result is achieved via a sliding clutch in the lower joint of the derailleur arm. If it is activated via the Shadow+ lever, the pressure on the pivot joint increases.

This increases the rotational resistance in the joint and thus counteracts the movement of the arm, which would otherwise rotate forwards more easily against the direction of travel in the event of vibrations. An explanatory video is available here.
