のだ is structurally similar to the English "It is that...". It consists of the sentence-nominalizer の and the copula だ, forming a noun predicate whose subject remains implicit. The な is the copula of the subordinate; if the subordinate ends with a verbal predicate, adding なのだ is not grammatically correct, it should be just のだ.
As for how to translate it when used as a simple speech pattern, that depends on the context, on whether it's used grammatically and semantically, and ultimately on stylistic choices.
