You must deactivate the bombs before they explode. You have to do it in order, with a limited time and jumping when there's no other way to advance. You have a limited amount of jumps available, and also less than 10 seconds to deactivate each bomb. And the floor will disappear under your feet as you advance!
Arrow keys to move, space bur to jump. The next bomb to be deactivated is the one that is in countdown.