The other replies are massively overcomplicating things. A monoid is - a set `X` - together with an associative binary operation (let's call it `+`) - and an

The other replies are massively overcomplicating things. A monoid is - a set `X` - together with an associative binary operation (let's call it `+`) - and an element (`0`) such that `a + 0 = 0 + a = a` for all elements `a` in `X`. Monoids are a class of structures, the collection of all arrays of a given type (with concatenation as the monoid operation, and the empty array as its identity element) is a particular example of a monoid. Other examples include the natural numbers under addition, the integers under multiplication, functions `T => T` under function composition, booleans under and, booleans under or, and strings under concatenation. They're one of the simplest and most common algebraic structures.