Hard Styler, it's not diificult for me to give you an explanation - I have a bad back and feel it when I don't do this. I'll explain a bit more. NB: Please understand that I am not a medical doctor and my explanation might not apply to you and your issues.
First of all, what Mark said is absolutely true. I want to add that different movements mean different things to your lower back. In a standing overhead press, especially with double kettlebells or a barbell, there is a real temptation to lean back. Indeed, most people do lean back at least a little, even if they don't realize it, once the load reaches a certain point. This leaning back can put your lumbar spine into extension, and you want to try to keep your lumbar spine in a neutral position and not extended when under that sort of load. Clenching your glutes will effectively turn your pelvis under a bit, removing some of that extension (or hyper-extension if you want to call it that).
Similar things happen for me in the bench press - in my case, my lumbar spine is somewhere between a little stiff and downright sore after a bench press set with a big back arch, but clenching my glutes again takes the edge off the compression in my lower back and, indeed, I feel like it helps me open up my spine in the right way and sometimes achieve an even bigger and better arch. And whether or not it's a bigger or better arch, it sure doesn't hurt as much.
In a nutshell, clenching your glutes tends to both get your lower back into a good place _and_ help brace it to maintain that position against forces trying to make it move - both good and necessary things in most lifts.
Just my opinion, your mileage may vary.
-S-
