I've heard the terms "edge ring" and "edge loop". What do they mean and how are they different?
An edge loop is a series of directly connected edges:
You can select an edge loop with AltRMB.
An edge ring is a series of edges which are not directly connected, but share faces:
You can select an edge ring with CtrlAltRMB.
As a bonus, you can run the select edge loop or the select edge ring operator on every selected edge automatically by pressing Edge loop or Edge ring in 3D view > Header > Select.