A ring is like a special kind of playground where you can add and subtract different numbers, kind of like how you play with different toys on a playground. A finite ring is like a playground where we only have a certain number of toys to play with, and once we run out of toys, we can't add any more.
So let's say we only have three toys in our finite ring: a red ball, a blue ball, and a green ball. We can add and subtract these balls in different ways. For example, we can add the red and blue ball to get a purple ball, or subtract the green ball from the red ball to get a yellow ball.
But once we've used up all of our toys, we can't add any more to our ring. So if we try to add a yellow ball and a pink ball, which we don't have, we can't do it because our ring only has three toys. This is what makes the ring "finite" - we have a set number of things to work with, and we can't add any more.