Oxygen is a gaseous element and is currently present in the atmosphere of only two bodies in Kerbal Space Program: Laythe and Kerbin. The element is important for air breathing engines on planes. Liquid fuel engines do also need oxygen but get it from oxidizer which is usually stored along with the liquid fuel in liquid fuel tanks.
Once the atmospheric pressure on a planet or moon with oxygen present is above the pressure required for air intakes, jet engines will become able to function with the oxygen is being supplied as intake air. Although jet engines do work on Laythe, reaction engines are required to get there (see a tutorial to get to laythe).
- Oxygen on Wikipedia