Despite the reputation of "rocket science" as a frightfully difficult subject that only the cleverest people can understand, the basic principle behind a rocket is actually quite simple.

Physicists talk about something called "momentum" which is what you get when you multiply the mass of an object (you can think of this as sort of like its weight) times its velocity (basically its speed). This is useful because it turns out that one of the basic laws of physics is that the momentum of an object will stay the same unless the outside world somehow acts upon it. Most of the everyday examples you can think of where something starts moving around are because there is some force acting on that object. For example, if you are standing but then start walking, your momentum increases (because your speed goes from zero to however fast you walk around) because you push on the ground with your feet and that propels you forward. Similarly, when a bird flaps its wings, they push down on the air around them and the resistance of the air powers the bird's flight.

But outer space is a vacuum without ground or air to push against, so there is no way for a spaceship to change its momentum by pushing back on its surroundings. Instead, a rocket burns fuel, which produces gases, and these gases are expelled from the thrusters at the back of the rocket. This causes the rocket to lose mass, so, for the product of mass times speed to stay the same, that means that the speed must increase exactly in proportion to the amount of gas lost. This allows the rocket to fly through the vacuum of outer space. It's the same principle that a squid uses to jet through the ocean, and if you've ever untied a balloon and watched it shoot around the room as it deflates, you've seen the same thing at work there too. Of course if you are sending a rocket to the Moon you have to control this process very precisely so that it doesn't fly every which way like the deflating balloon, and doing that is why rocket science is difficult.