Imagine you and your friend are sitting in a toy car that moves forward when you push it. When you push the car, you move backward a little bit, but your friend stays put in the car.
Now, let's pretend you and your friend are both really heavy and the car is super small. You push the car forward as hard as you can and again, you move backward but your friend barely moves because they are so heavy.
In this situation, it might be helpful to imagine a special frame of reference where the center of the car is always the same. If you and your friend move forward together at the same speed in opposite directions from the center of the car, then the center of the car won't move at all. This is called the center-of-momentum frame.
Scientists use this frame of reference to study objects that are moving really fast or have a lot of energy. By using the center-of-momentum frame, they can more easily compare the movements and energies of different particles.