The launching of rockets into space has everything to do with Newton's third law of Intertia. He states that every force exerted will have an equal and opposite force. So, lets begin.
With this law as our basis, we can conclude that the force exerted on the ground by the burning fuel of the rocket will in turn lead to an equal but opposite force pushing off the rocket. So, the reason why rockets are able to be launched into space is because the fuel that is inside it is exerting much energy on the ground, leading to an equivalent resultant force.
That said, there is a problem we face, the force exerted by gravity, which is 10N. Gravity is acting against the rocket itself, thus making it more difficult to be launched into space. However, Robert Goddard thought of an excellent plan, which is used in the present as well.
He believed that it will be possible to store fuel in 2 or 3 different stages, which is another term for the each portion carrying fuel in it, and launching it into space. So when 1 stage runs out of fuel, it can be thrown away by releasing it into space. This way, the weight that the fuel needs to push against gravity will decrease and it is much better than the conventional method, which uses the only one stage to store all the fuel.
This theory can be applied to the aeroplane as well. As engines in the airplane suck up the air, and exits at the end, there is a force exerted on the atmosphere and the resultant force pushes the aircraft forward. With a decreasing area of the engine inside, the air speeds up and exits the other end, giving it additional speed which helps to accelerate the aircraft.
Sources --> http://www.suntrek.org/solar-spacecraft/satellites-rockets/how-rockets-work.shtml
