This is the standard concept. Heuristically, if we have a space "M" for which each point "m" ∊ "M" corresponds to an algebro-geometric object "Um", then we can assemble these objects into a tautological family "U" over "M". (For example, the Grassmannian G("k", "V") carries a rank "k" bundle whose fiber at any point ["L"] ∊ G("k", "V") is simply the linear subspace "L" ⊂ "V".) "M" is called a base space of the family "U". We say that such a family is universal if any family of algebro-geometric objects "T" over any base space "B" is the pullback of "U" along a unique map "B" → "M". A fine moduli space is a space "M" which is the base of a universal family.