This だ is a copula. It's a plain form of the copula - copula has similar forms as verbs. You may know its polite form as well - です (warning though - です is not only a copula, it may also be just a marker of polite speech level). それはとってもいい話です。 is the polite version of the same sentence.
Copula doesn't really act on the noun, rather it links the subject それ with the predicative expression とってもいい話 and gives it a meaning of equivalence (in this case): This is a very good story. Japanese copula has similar meaning to the English verb "to be" (as in X is Y meaning X = Y or Y describes X).
それはとってもいい話 on its own is not a regular sentence in Japanese as it doesn't have a predicate.. Copula can be used as a predicate to finish off sentences as in this example. You could change this sentence to use いい as a predicate and not use copula as in
Just to clarify: there are sentences (minor sentences) without predicates that are used commonly in casual speech, newspapers, titles, etc. Predicates, including copula, can be omitted in those kinds of sentences but cannot be in a regular (major) sentence.