Oxygen is an element and is 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 three bodies in Kerbal Space Program: Laythe, Kerbin, and since 1.0 also the Sun. Once the atmospheric pressure on a planet or moon with oxygen is above the pressure required for air intakes, jet engines will become able to function with the oxygen that 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 units of oxidizer for 9 units of liquid fuel. Jet engines use 15 units of intake air for 1 unit of liquid fuel.
- Oxygen on Wikipedia