The function of the Hospital is to heal your troops wounded in battle. The treatment of wounded troops costs half the time and resources needed to train new troops, so it is a good idea to have as large a Hospital Capacity as possible.
You can achieve this by building more Hospitals and upgrading them.
Research at the Lab as well as Chief Talent Points can also increase your Hospital Capacity and Healing Speed. Be sure to heal your wounded troops because when your Hospital Capacity is reached any further troops wounded in battle will be lost.
What happens to your troops after a battle will vary depending on the kind of battle: When you are defending, all wounded troops will be sent to the Hospitals until Hospital Capacity is reached, after which they will be lost.
When you attack Infected, a small percentage of troops will be wounded and sent to Hospitals. When you attack an opponent on a resource tile, wounded troops will be sent to the Hospitals until Hospital Capacity is reached. When you attack an opponent’s Settlement, ALL wounded troops will be lost.
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Game Guide for State of Survival: Survive the Zombie Apocalypse