What are the 'parts' to a mechanical disc brake set?
It depends on how you buy the brake, so you need to check whats coming with what you're buying. Typically, you get the caliper+pads+rotor+mounting hardware and buy the brake lever (which is a V-brake lever most of the time unless its a road brake in which case its a regular short pull lever) separately along with the cables+housing. In some cases though (esp. buying brakes on eBay), people buy just the caliper+pads+mounting hardware and get rotors separately.

This example from Nashbar tells you the Avid BB7 Road comes with "Includes 1 post mount (74mm) caliper, 1 rotor (160mm) with bolts, sintered pads, and 74mm post mount to IS mount adapter".

The typical hardware (Avid BB7 Road with a G2 rotor) is shown below:


(from Nashbar)

To this you'd need to add a brake lever (e.g. Tektro RL340), some brake cable and brake housing in order to get a functioning brake system. 

For maintenance and some description of the important parts, see this Park tool repair guide as well.