SOLDIER is this elite unit in the ShinRa military. Those who get into it, especially those at the higher ranks, have been enhanced thanks to Mako energy infusion.

[And other things as well, but even with his knowledge of the future Cloud doesn't know all the details.]

I left home and went to Midgar hoping to join SOLDIER, be a First Class like my hero. When I got there they pretty much immediately told me I was no good and I just wound up as an infantryman. If it wasn't for Zack and that Turk I probably wouldn't have lasted long either.