In my opinion the gmat shows 3 things. 1. How well you can focus. In the end it's a 4 hour test. It is 4 hours of having to focus with very little breaks. I never had any issues focusing at school but I was unable to form a straight sentence after taking the gmat. If you have issues focusing or staying concentrated for longer periods of time you'll have issues with the gmat.
How good you are at solving problems. Big problems. The GMAT can be seen as one big problem. You have to identify what the problem is (e.g. your weak areas), how to improve them (e.g. identify the right studying methods, come up with a time schedule) and then finally you also have to pull through and actually improve them.
How good you are at standardised tests. There are people that are good at standardised tests and there are people that suck at them. I don't think it indicates whether you'll succeed in business school or whether you'll be successful in life. It just states whether you are good at a certain type of test.
Obviously there are a couple of other factors that play into your performance but I felt like that is what the gmat most accurately measures.