Just a big, and probably dangerous, bonfire at the beginning. This is your town HQ and the first construct you open. Its level determines both the max level you can upgrade other buildings to along with which buildings you can open up and when you open them up. Upgrading it will increase the amount of heat it produces and also increases your power.
The Town Center has a secondary function that is equally as important:
Keeping your Survivors warm during the day, night, and during snowstorms.
This helps prevent your Survivors from becoming sick. When sick, your Survivors will not be able to work until they are well again.
