When a dry wall rasp is pushed or pulled along the cut edge of a piece of plasterboard, the teeth on the rasp’s blade cut away the rough surface on the cut edge.
It works much like a cheese grater on a block of cheese.
Like a cheese grater, dry wall rasps can have either a fine-toothed, or coarse-toothed blade. A fine-toothed blade will give a smoother, better-quality finish to the edge of plasterboard that will allow you to more accurately butt the sheets of plasterboard together. However, they will take longer to achieve this finish, requiring more passes along the edge of the plasterboard and so more effort.