What is the PHP operator % and how do I use it in real-world examples?

It's the modulus operator, which gives the integer remainder of a division e.g.

7 / 2 = 3.5  // 3 remainder 1
7 % 2 = 1    // the remainder

Obvious real world example is working out whether a number is odd or even

if (($n % 2) == 0) the number is even, else it's odd... useful when you want to show alternate rows in a table in different colours