Liquid oxygen is also used as an oxidizer in rocket engines. On Earth, things burn because there is oxygen in the air around us. However, rocket engines are used in the upper atmosphere and space where there is little or no air. So, the oxidizer has to be carried with the engine. This causes many problems, as pumping mechanisms and cooling strategies are required since oxygen is only liquid below -183 Degrees Celsius.
Robert Goddard used liquid oxygen in 1926, when he tested the first liquid propellant rocket engine. In doing so, he solved several problems. One of these was the fact that propellant (gasoline, in this case) and oxidizer had to burn together at a sufficiently high rate to produce thrust. When liquid oxygen is heated above -183 degrees, it vaporises and expands. This causes a very high pressure to build up in a closed container. Goddard used this pressure (increased even further by heating the liquid oxygen with an alcohol burner) to push the oxidizer and propellant at high pressure simulatenously into the combustion chamber. Here, they mixed and burned, producing thrust.
Robert Goddard's rocket reached an estimated speed of 60 miles per hour and reached a height of 41 feet. It flew for 21 and a half seconds. This paved the way for further use of LOX in rocket engines. It was used with alcohol in German V2 rockets, with kerosene on the first stage of the Saturn V and is used with liquid hydrogen for the Space Shuttle Main Engines.