The leftovers.
What is left over when a number doesn't divide evenly.
Modular arithmetic is entirely based on remainders.
The remainder must always be smaller than the divisor.
Plain English: Sometimes things don't fit perfectly. If you have 5 candies and 2 friends, each gets 2, and 1 is left over. That '1' is the remainder.
Real-world example: Packing cars for a trip. 13 people, 4 seats per car. You need 4 cars (3 full, 1 with just 1 person).
Writing 'R5' if you are dividing by 4. If remainder > divisor, you did it wrong!