That is surprising. They show up all over in fairly common libraries - for instance, Writer collects a monoidal value. The very simplest notion is "monoid is for things you can combine". Taken from math, a monoid is a set of things (a type) for which you have an operation (called mappend in Haskell) which you can combine associatively, where the set contains an element (mempty in Haskell) that is an identity with respect to that operation.

Some common monoids are:

    Anything list-like:
        mappend appends two lists
        mempty is the empty list

    Integers over addition (newtype Sum)
        mappend adds two integers
        mempty is zero

    Tuple of monoids:
        mappend is componentwise mappend
        mempty is (mempty, mempty)

    Functions where the domain and range are the same:
        mappend is function composition
        mempty is id