One of the main contributing factors is that air becomes less dense the higher you go, therefore drag on the airframe reduces. Less drag aids engine efficiency.
Along with the other two answers about drag, the ratio of fuel to air remains the same. Therefore less dense air requires less fuel.
Aside from the thinner air being less draggy on the airframe the fact that this air is also very cold also helps with engine efficiency.
There is less air pressure and as a result less drag on the airplanes. The result is less fuel is required to maintain the speed.