As an aeroplane moves through the air, the air passes over the surface of its wings. These wings are shaped with a curved top surface and a flatter lower surface, which means that air passing over the top of the wing has to travel a little faster than that below the wing.
This causes the pressure to lower above the wing, while the air pressure below pushes up. The end result is the lift that keeps the aeroplane in the air.
The tail surfaces of the aeroplane keep the wing at the proper angle to provide the right amount of lift. The power to propel the aeroplane along can come either from the engine, or, in the case of gliders, from rising air currents.
Jet engines propel a plane just like a rocket, with a stream of hot gasses.