“Throwin’ Down” is an old-time expression for drawing a handgun—typically a revolver—and demonstrably aiming the piece at a live target.
Terminology: Hammer Spur
Times are a' changing. Not so long ago, almost every handgun hammer had a spur. This is the rearmost visible extension of the hammer on a pistol or revolver. It's the part on which the shooter places his thumb in order to cock the gun's action.