The Infirmary determines your retreat rates after the mission is complete. This building level is key for players that wish to colonize the map at a rapid rate.
The level of the Infirmary will determine the retreating speed of your troops. Though Boosts from the Weapons Depot can be used to increase the speed of a mission or invasion, it will not affect the time it takes for troops to retreat back to base. Only the Infirmary level has a direct impact on the speed for troops to retreat back to your City.
This building is an offensive building, meaning you will have a slight increase in Attack Power during an invasion