Let's try a few examples. What is 21 mod 4? In other words, what is the remainder when you divide 21 by 4?
Four goes into 21 five times, with one left over, so the remainder is one; we can write 21/4 = 5r1.
Let's try a more challenging one: what is 187 mod 12?
12 goes into 18 once, with six left over; it then goes into 67 five times, with 7 left over, so we get 187/12 = 15r7, and the remainder is seven.
Finally, what is 120 mod 10?
Ten goes into 120 twelve times, with nothing left over; that is, 10 divides 120. This means that 120 mod 10 = 0, and there is no remainder.