Actually, the c is for skinny. More or less. It was originally a French size. By their system, the number was roughly the OD of the tire, A was a fat tire, B was medium, and C was skinny. The whole modern sizing thing is a crazy mix up of the remnants of various older systems.
Tire Sizing Systems
EDIT: There are also 700c tubular tires and rims (glue on, not clincher).