A rocket is a big rocket that goes really fast and really high. The gas-generator cycle is how some rockets work to make all the fire and smoke to push the rocket up into the sky.
Inside the rocket, there's something called a combustion chamber. This is where all the fire happens that makes the rocket go up. But, to make the fire, you need something called fuel and something called oxidizer.
The gas-generator cycle works by using some of the fuel and oxidizer to make a little tiny fire in something called a gas generator. The little fire in the gas generator makes a lot of hot gas that goes into the combustion chamber and helps make the big fire that pushes the rocket up.
So, basically, the gas-generator cycle is like a little helper that makes a little fire to help the big fire that makes the rocket go up really fast and really high.