When sawing and drilling, you create burrs and sharp edges on your workpiece that need to be removed; rasps and files take care of these. Using a rasp or a file is often the first step in finishing a project, or prepping a material for the next step.
Step 1: Identifying Files and Rasps
Flat rasp - has large, coarse teeth to quickly remove material
Flat file without a handle - allows you to remove burrs and rough edges
Multi-use rasp and file - has two files and two rasps on one tool
Fine flat file without handle - this tool is for finishing and scratch and gouge removal
Triangle file - allows you to get into corners and clean up edges that have notches
Small round file - cleans small round holes and inside curves
Medium round file - as above, but with coarser teeth
Large round file - as above, but coarser still
For more information:
Wikipedia Rasp Entry
Wikipedia File Entry
Briefly, a file is for detail work while a rasp removes larger quantities of material.