The remainder is what is left over after dividing an integer by another integer and want an integer result
On your calculator, if you divide 13 centimeters by 4 it will show the result as 3.25, which is correct. But if you are doing arithmetic where you want the result to be an integer, the result is 3, but with 1 left over. This is the remainder.
This happens in real life when you are using whole or counting numbers. For example if you have 13 oranges and want to divide them equally to 4 friends, you can give each of the 3 oranges, but with one left over. This is the remainder.
Formally: with a remainer of 1