WHAT IS THEN A MONOID?

To my understanding a monoid is a semigroup. In a semigroup the only property missing from a group is the inverse property. The elements in a monoid, it is said, need not have inverses. But I do not know why at this point. I will need to read more to see what kind of monoids are out there. The monoid, I know, must have an identity, as there is always an identity in every group. In a monoid as in a group, we have the associative property, as well as, the closure property. Thus so far as I can understand a monoid is a semigroup but as the need for not necessarily carrying inverses is not yet clear to me. I suppose that if in a monoid there are inverses, this is only a bonus. What makes a monoid different from a group is simply that a group has inverses for sure while in a monoid inverses can be absent.