Paper towels are made up of cellulose fibers, which also make up cotton, wood, and most other plants. These cellulose fibers are actually giant molecules that consist of many small molecules linked together.
Key To Absorption
The small molecules that combine to make up cellulose are sugar molecules; that's the key to the absorbency of paper towels.
Think how easily sugar dissolves in water. When you get a paper towel wet, the water molecules rush in and cling to the cellulose fibers. That's why paper towels are great at picking up spills.
Although cellulose contains sugar molecules, that doesn't mean paper towels are edible. We humans don't have any of the enzymes necessary to split the cellulose molecule apart into the individual sugar molecules. That's why paper towels have no nutritional value for us.
Sources and Further Reading:
Bloomfield, Louis A. "How Things Work" at http://howthingswork.virginia.edu/. Accessed June 29, 2002.