A vector addition system is like a game where you have some numbers or things called "vectors" and you can add them together. You can move them around and change their direction, but you always add them up to make a new vector.
Imagine you have some toy cars with arrows pointing in the direction they move. If you push one car with an arrow in one direction and another car with an arrow in a different direction, you add their arrows together to get a new arrow that shows where both cars would go if they moved at the same time. This is how vector addition works.
Vector addition is useful in lots of different things, like understanding how things move in physics or in making computer simulations. It helps us understand the direction and speed of everything happening around us.