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A happy number is one in which you square the digits and sum the answers. Repeat the process and keep doing so. If the answer reaches 1 then it is stuck at 1.
For example, consider 23
2^2 + 3^2 = 4 + 9 = 13
1^2 + 3^2 = 1 + 9 = 10
1^2 + 0^2 = 1 + 0 = 1
So 23 is a happy number.
A sad number - better known as unhappy number - is one that does not ever reach 1.
Consider 24
2^2 + 4^2 = 4 + 16 = 20
2^2 + 0^2 = 4
4^2 = 16
1^2 + 6^2 = 1 + 36 = 37
3^2 + 7^2 = 9 + 49 = 58
5^2 + 8^2 = 25 + 64 = 89
8^2 + 9^2 = 64 + 91 = 145
1^2 + 4^2 + 5^2 = 1 + 16 + 25 = 42
4^2 + 2^2 = 16 + 4 = 20
and we are back to the first step. From here on, the sums of digital squares will keep cycling through these numbers and so cannot ever reach 1. So 24 is a sad number.
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