Primitive recursive arithmetic is like counting and doing simple calculations in a special way. Think of it like having a set of rules for how you can count and add numbers.
For example, one rule might be that you can start counting from 0 and add 1 each time to get the next number. Another rule could be that you can add two numbers together to get a new number.
With primitive recursive arithmetic, you can use these rules to solve simple math problems, like 2 + 3 or 5 x 6.
But you can only use these specific rules - you can't make up new ones on the spot. This is what makes it "primitive" - it's a basic set of rules that you follow.
It might not be enough to solve every math problem you come across, but it's a good starting point for understanding math and building more complex calculations later on.