It's highly experimental and we are still trying to do green propulsion engines. All of these engines basically take a fuel, make it explode inside with very fast air going through as well, and throw it out the back to generate thrust. The usual fuel for aircraft would be hydrocarbons, aka oil derived fuel. It's basically a slightly modified kerosine.

Hydrogen can still combust (or explode) in the presence of air. It's actually what made the original space shuttles able to get out of the atmosphere. The exhaust is mostly just water, as H2 + O => H2O (water). Whether this specific strategy will get off the ground is too early to tell (pun intended).