Definition
This isn't a golf club, but rather a technique where a golfer hits a putter from off the green, typically from the fringe.
Usage
You're gonna need a Texas Wedge for that one!
Origin
Since Texas is known for hot, dry, and firm conditions which are difficult to hit chip and pitch shots off, the Texas Wedge became a replacement for hitting those difficult shots. Instead, the golfer can hit a putt, which is a much easier shot.