Spawn is a mechanic that is used by the Virus. More specifically, it is the mechanic that allows Maggots to be brought into play. If a structure says that it "spawns X Maggots" (where X is a number), that means that during each Virus prep phase, X new Maggots should be placed in the same location as that structure. New maggots should always be placed face-up and ready.
The engagement of the structure does not matter, nor does it matter if the structure is currently researching an upgrade. This is one of the few actions in the game that a card can perform before finishing a previous action. It is also one of the few actions in the game that can occur without engaging a card.
Spawning is not mandatory, though it is almost always beneficial to do so. If there are not enough Maggots in the Virus deck during a prep phase, the Virus player may distribute the available Maggots however he chooses.
Spawning does not occur during other players' prep phases.
The Virus player controls a Stagnant Reservoir and a Festering Corpse in his base, as well as a Festering Corpse in his opponent's low ground. During his next prep phase, he may place up to 3 new Maggots in his base, and 1 new Maggot in his opponent's low ground.