When you are in a hurry and you want to quickly determine, if a number can be divided by 2, 4, 6, 7, 8, 9 without long division then divisibility rules comes into rescue where you can test easily if one number can be evenly divided by another.

Divisibility means that you are able to divide a number evenly.

Divisibility rule is used to check whether a given number is divisible by a fixed divisor by examining its digits.

To illustrate the concept, Suppose you are in a coffee shop and you have ordered 8 cups of coffee. You and your 3 friends wish to have 2 cups of coffee each. Suddenly one of your new friend join in, then he will get less coffee and there is no way you can share your coffee evenly.
In general, a whole number x divides another whole number y if and only if you can find a whole number n such that
x $\times$ n = y
For example, 24 is easily divisible by 3 because 3 times 8 is equal to 24.