Sometimes I use terms so basic to me that I forget to define them. Oops.
A girth (English) or cinch (western) is the broad strap that goes under the horse's belly and holds the saddle in place. It's one of the most important pieces of tack - if your girth breaks you're in a lot of trouble.
The English girth buckles under the saddle strap. The saddle is supplied with three girth straps or billets, of which two are used (the other is a spare, in case one of them breaks).
Western cinches are secured with a single latigo - I guess cowboys are less worried about the girth separating from the saddle (and thus the saddle and rider from the horse).
Front and back cinches can be seen on these western trail horses.