Destroy enemy labs is a winning objective in both singleplayer and multiplayer games. It simply requires the player to use any means possible to destroy the enemy player's Lab, therefore eliminating them from the game. In such scenarios, destroying the lab will also make all of that player's units and buildings disappear almost instantly.
This objective differs from Destroy enemy base in that only the lab needs to be destroyed.
In the Original Campaign, the enemy allways has this objective in regards to the player.