Emergence holes are holes that appear in the ground that the Locust use to reach the surface and attack. In addition to being useful for an ambush, the holes can also collapse structures, if opened near one (an example being a pillar holding up a stone roof). In the game, the player can close these holes either by throwing a grenade into them, or by killing every Locust that comes out.
One should be cautious near Emergence Holes, as opening Emergence Holes cause damage and can even kill you.
In Gears of War 1, there are a few areas where you have to close a number of Emergence Holes before you can proceed. The easiest way to finish these "checkpoints" is to use your grenades on emergence holes as they appear (usually one at a time, though sometimes in pairs or opening up close enough together in time to feel like a pair).
Up until Gears of war 2, Emergence holes have been useless against the hard granite landscape found in Jancinto, the last safe heaven for Humans. However in Gears of war 2 the Locust have new powers which allow them to create emergence holes the size of cities, which poses a huge threat to Jancinto and is the basis for the story.