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There are two parts to the despawning system, both are meant to reduce mob count and manage lag.
The first part is simple, it just makes it so no spore mobs will spawn if there aren't players in the world. This is meant for servers.
The second part is more complex, but essentially each tier of spore mob has a maximum number of individuals from that tier that can exist in the world. Every minute, the despawning system will count the mobs in the world based on the mob tier. If there are too many mobs from any tier, the system will despawn the ones farthest away from a player. List of tiers/mobs and their max number of individuals:
Infected - 60
Evolved - 35
Hyper Evolved - 20
Organoids - 40
Scents - 30
Some mobs are specifically ignored by the despawning system, via a changeable list found in the config. Scampers, Gastgebers, Specters, Infested Constructs, Wombs, and Proto Hiveminds are all ignored by the despawning system.
Note the 30 Scent limit is different from the local Scent cap.
Additionally, there is a basic mob cap that makes it so only 40 Infected can spawn naturally (in the dark normally).
Organoids also have their own custom method of despawning to prevent lag and overcrowding, explained on the Organoids page.
Trivia
A common issue with lag from the mod is mob count, with there often being hundreds or thousands of spore mobs. The Despawning System was made to stop the majority of that lag, and to be able to run an official spore Minecraft server.