A rocket's real job isn't altitude, it's sideways speed. Orbit means moving so fast horizontally (about 28,000 km/h) that as gravity pulls you down, the ground curves away beneath you. You fall forever and keep missing.
Stages are the trick that makes it possible: burn the fuel in the bottom section, then drop the dead weight and let a lighter rocket keep accelerating. Each discarded stage buys more speed for what remains.