A few purposes:

Castle garrison as other mentioned already. 1 peasant unit keeps even a citadel in the green levels and is enough to make the enym waste turns sieging your castle/fortress/citadel.

Town garrison. Your towns can only upkeep certain amounts of militia for free. Additional militia has full upkeep besides a higher training cost. Especially for inland garrisons, you can replace excess militia with peasants for even less upkeep and same effect.

You can also tag em along in their own stack behind an invasion force so you can garrison towns along the way quickly and cheaply. This is because towns you capture have their pools depleted for a turn or more, which can stall your invasion army unless you want to leave a general behind or have the settlement revolt.