Burning villages is an important part of keeping the world safely not overpopulated. Burning a village gives silver to the burner, based on the score of the burnt village at a 1:1 ratio.
Villages cannot be claimed and then burned immediately. The player must send a missionary from a Church to one of their own villages and it will be cleansed with holy fire. The missionary cannot target the village it was recruited in.
Burning a village is an opportunity cost, and depending on how populated the world is, a multiplier may be enacted to increase the profitability of burning a village.