The Zerg, "Zerg Rush" or "Zerging" are slang terms referring to a very large group(s) of soldiers that make up the primary attack front of an empire. Most of the time the Zerg are unorganized, but there are so many soldiers that they are able to effectively push the front via sheer force of number.
The term's origin comes from the real-time strategy game Starcraft, which features three playable races: one of them is called Zerg. Zerg units are much weaker in general, but are cheaper than their comparisons and require less time to build. Hence, the Zerg compensate by sheer numbers. The generalization of this origin comes from the Zerg strategy to just create a lot of Zerglings (the weakest but also cheapest & fastest unit they can build) and attack the enemy base before they have any defenses up. In Starcraft this is better known as a Zerg rush, but has spread to other games in its shortened form.