The Composter uses a compost barrel to create compost (the item). It works like bone meal to increase the speed of plant growth. The Florist must have compost to grow flowers. The Farmer does not need compost or bone meal to work, but prefers it (this is toggleable in the Farmer’s Hut GUI).
Composted dirt can be crafted by the Farmer. It is used in the Flower Shop schematics.