Farms can be found outside the castle walls. They produce the food needed to attack other players or raid caverns in the dungeon. Since a farm stops producing once its storage capacity is exhausted, it makes sense to transfer the stored food to the silo by tapping the farm.
The number of farms is limited by the level of the throne room. Two farms are available right away, the third when the throne room reaches level 2, and the fourth at level 4.
With higher levels farms can produce faster and store more food. In the beginning, farms can be one level higher than the throne room. They are eventually maxed out at level 19. The maximum level that the Farms can reach depends of the current level of Silo.