To elaborate on seiferteric: If the engine were just an unducted fan, the input and output volumes and velocities would be the same, and if they're pointed in opposite directions, there would be zero net force.
In a jet engine though, you have a nozzle on the back, so the input area is greater than the output area. Heating the air also causes it to take up much more volume. These put together, mean that the output velocity is much greater than the input velocity, so there is a momentum transfer from the atmosphere to the plane.
In a jet engine though, you have a nozzle on the back, so the input area is greater than the output area. Heating the air also causes it to take up much more volume. These put together, mean that the output velocity is much greater than the input velocity, so there is a momentum transfer from the atmosphere to the plane.