Destructible cover is anything that shields a player from harm, but can be destroyed by enemies or other players. It's most common in third-person shooters like Gears of War, but it can be implemented even in games without a cover mechanic. For example, in the Battlefield games built on the Frostbite Engine, even buildings are destructible, so players can't let their guard down even when they would be safe in most shooters.
The earliest use of destructible cover in games was in 2D shooters, most notably Space Invaders, which has destructible barriers that the player can hide behind. Deployable cover, such as in the Halo franchise, can usually be destroyed.