Why does a rocket launch?

A rocket does not push against the air or the ground. Inside the combustion chamber, fuel and oxidiser burn at high pressure and the hot gas escapes through a nozzle at several kilometres per second. Expelling that mass rearward gives the vehicle an equal momentum forward. The resulting force, thrust, equals the mass flow of exhaust multiplied by its velocity, plus a small pressure term at the nozzle exit. Because the reaction comes from the exhaust itself, the principle works just as well in vacuum, which is why rockets are the only practical way to reach orbit.

On the pad the rocket only lifts off when thrust exceeds its weight. The ratio between the two, the thrust-to-weight ratio, is typically between 1.2 and 1.5 for large launchers at ignition: a Saturn V produced about 34 MN of thrust against a weight of roughly 28 MN and left the pad slowly, gaining speed as it burned propellant and became lighter. Engines are usually ignited a few seconds before the hold-down clamps release so that controllers can confirm all of them are running at full thrust.

The launch is only the beginning of the job. Reaching orbit requires a horizontal speed of about 7.8 km/s, so after a short vertical climb the rocket pitches over and spends most of its burn accelerating sideways. Stages are dropped as their tanks empty to shed dead weight, and the upper stage fires until the vehicle is moving fast enough that its fall towards Earth matches the curvature of the planet. Everything about a launch, from the choice of propellants to the steep initial climb, follows from the need to convert stored chemical energy into that speed as efficiently as possible.