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Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

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Soft question: beginners reference to moduli spaces

For moduli I would second Geometry of Algebraic Curves, Volume II. For a clear introduction to stacks, I like Martin Olsson's book "Compactifying Moduli Spaces for Abelian Varieties". A good motivati …
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