We recently got a Glute Ham Developer at our gym. Ok, so lemme tell you the short version...it is AWESOME!!!
The longer version is that it provides a host of ways to strengthen your hip extension power which is the primary driver of explosive total body power and functional strength. That's on top of the fact that at its core, this is a bodyweight strength based apparatus and each exercise that can be performed on it must first be mastered with your bodyweight before moving on to weighted versions.
The hips are what drive dozens of crucial athletic moves such as:
Beyond that, the hips are what drive primary lifting strength when lifting and object from the ground. The hips and core are truly where you make or break your functional strength.
You can have strong arms and legs but if your hips and core are jello then there is nothing to tie it all together and make it actually work in any kind of integrated functionally useful manner.
A list of just a few of the excellent exercises that can be performed on the Glute Ham Developer: