The idea is you can burn the fuel for the first 10km or so using air as the oxidiser, and only when it gets too thin do you need to use LOX (liquid O2) or high-test peroxide, etc, for getting in to your wanted orbit.
While 10km or so might not sound like much for the 100km or more "orbit" hight, it represents a lot of the volume of fuel burned and so the saving in not having to carry your oxidiser on-board is very significant. See also:
https://en.wikipedia.org/wiki/Propellant_mass_fraction