Consider these equations for integers:

    x * 1 = x
    1 * x = 1
    x * (y * z) = (x * y) * z

These should be familiar if you know about integers.

Now consider the following equations for strings:

    concat(x, "") = x
    concat("", x) = x
    concat(x, concat(y, z)) = concat(concat(x, y), z)

These should be familiar if you know about strings.

Now consider the following equations for booleans:

    x or false = x
    false or x = x
    x or (y or z) = (x or y) or z

These should be familiar if you know about booleans.

If you can see the pattern, you understand monoids. Monoids are everywhere in programming.