Step-by-step explanation:
in plain English :
a controlled explosion (by burning only one part of the fuel with one part of the oxygen in the tanks at any moment) over and over again produces gases with so much power and speed that the energy at the lower end (the mass of the gases expelled downwards create the equal counter effect of pushing the rest of the rocket upwards) overpowers the force of Earth's gravity that is trying to keep the rocket on the ground.
in other words, it is an extreme recoil effect, which principle we can see often in nature or with other products of engineering. like jet or propeller airplanes, boats and ships (e.g. oars in boats : we push with the oars the water outside backwards, and that impulse is transferred through our bodies into the body of the boat, which makes it go forward), shooting a gun, swimming in a pool or lake, simply running or jumping, ...
whenever we don't have to overpower gravity or other strong forces in the direction of our movement, much less energy is needed, and the recoil is much weaker.