<> is a placeholder for an operation (a function, really) taking two inputs, mempty is a placeholder for a special value, and x and y are placeholders for arbit

<> is a placeholder for an operation (a function, really) taking two inputs, mempty is a placeholder for a special value, and x and y are placeholders for arbitrary values. If you can find something that fits the pattern, then it is a monoid. Such as where <> is addition, mempty is 0, and x and y are numbers. Or where <> is string concatenation, mempty is the empty string, etc.