Oxygen is an element and required to burn liquid fuel. Itself is not a resource but there are two resources, intake air and oxidizer, which contain oxygen and can be supplied together with the fuel to jet engines and liquid fuel engines.
Oxygen is present as a gas in the atmosphere of only two bodies in Kerbal Space Program: Laythe and Kerbin. 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).
The other source of oxygen is along with the liquid fuel in liquid fuel tanks as oxidizer. It is fed to the liquid fuel engine in a mixture ratio of 11 parts oxygen for 9 parts liquid fuel. Jet engines use 15 parts intake air for 1 part liquid fuel.
- Oxygen on Wikipedia