There are many principles behind a rocket, and some of them will be explained on this page.
When a rocket launches, there are many things going on, things such as conservation of energy. If you aren't familiar with the law of conservation of energy it effectively means that energy can't be created nor destroyed, only transformed from one form to another. As an example of this let's look at a rocket launch.
Here we have an Atlas V rocket on the launch pad. Right now the tanks are full with fuel for the engines to burn when it launches. Right now there is an immense amount of chemical energy stored in this rocket. Chemical energy is the energy stored in the bonds of chemical compounds. But when the rocket launches, more specifically when the engines ignite, it converts the chemical energy into kinetic (movement) energy.
Rocket engines are very complex, so I will try my best to summarize how they produce thrust and how they ignite.
Here is a diagram of a typical rocket engine, now let me explain what's happening at the time of ignition.
First a small amount of propellant is ignited in the pre-burner. This creates energy that spins up the turbine. From there it powers the two pumps that begin flowing the fuel (most commonly kerosene and liquid oxygen) into the combustion chamber. This is where the two meet and ignite, the force from that causes there to be low velocity, high pressure gas. It is then forced through the small throat, and in doing that in coverts to high velocity, low pressure gas. So the thrust comes from that conversion that occurs in the throat.
There are many events that occur during the ascent, but the once I want to focus on is the atmospheric friction. In some pictures you'll see the rocket covered in orange plasma. This is the result of the vehicle hitting the atmosphere and causing friction. The friction creates the incredibly hot plasma.
Much like ascent, you will see the vehicle covered in plasma when it enters the atmosphere, it again is a result of intense friction between the vehicle and atmosphere.
Without centripetal force, there wouldn't be any rockets, because once they go up, they wouldn't be able to orbit. By definition centripetal force is a force that makes a body follow a curved path. Earth's gravity creates a centripetal force that captures an object in the gravity, but it doesn't weigh it down, meaning it orbits. So an orbit can be described as simply Earth's gravity pulling an object in a circular path around it.