A tuple is just an ordered bag of elements. E.G. a graph is a tuple (V, E) where V (vertices) is a set and E (edges) is a binary relation between vertices.

Defining stuff as tuples makes sense, because then you can define the set of all such tuples (e.g. the set of all monoids for a given set M or the set of all graphs for the given vertices V) and formally reason about it :)