Witt vectors are like a special kind of number that helps you describe how things repeat. Imagine you have a big bag of marbles, and you want to know how many red marbles you have in every 2nd, 3rd, 4th... 10th, and so on marbles. Witt vectors can help you count all of these things at once, and you can also use them to do other fun things like addition, subtraction, and multiplication just like regular numbers!
But instead of just counting things like marbles, Witt vectors can help you count things that are more complicated, like patterns of numbers or shapes. They have a special way of combining and adding things called "component-wise operations" which makes it easy to do math with them. So, just like you might use addition and subtraction to do math with regular numbers, you can use these operations to do math with Witt vectors.
Overall, Witt vectors are a really cool tool that mathematicians can use to study things that repeat in different ways. They are especially helpful when studying things like algebra and geometry because they can help simplify complex problems and give us deeper insights into how things work.