These buildings house your Survivors giving them a place to rest, relax, and sleep. As of this writing, a maximum of eight Shelters can be built.
As you upgrade the Shelters and furniture inside them, the amount of Survivors that can join your town increases up to a maximum of 32. Upgrading the Shelters increases Survivor Sleep Quality, Comfort, Mood, and Warmth along with a boost in power. You will need to max out the upgrades of certain furniture inside the building before being able to upgrade the building to the next level.
Keeping these buildings and the furniture inside them upgraded as much as you can is important for the health and happiness of your Survivors. Until you get your Clinic built, your Survivors will come back here if they get sick.