In んです, the ん is a colloquial (spoken) form of の. You may see some grammar resources talk about the “explanatory の”, which is what this is.
When you add のだ to the end of a sentence, you are turning the sentence into a noun (using の), and then make it into a “subject is noun” sentence by adding だ (or です).
Consider the following in English:
“My car stopped working.”
“It is that my car stopped working.”
The latter is a “subject is noun” sentence, where “it” is the subject, and “my car stopped working” is the noun that “it” is.
The latter sentence isn’t quite how we’d word English, but even so it may sound a bit like it’s giving an explanation. “Why were you late to work today?” “It is that my car stopped working.” (In English, we’d more likely use the word “because” and say, “It’s because my car stopped working.”
のだ works the same in Japanese; it’s essentially giving a reason (or, in the case of a question, asking a reason).
I wrote a bit in depth on のだ here, including on how it’s used in Japanese, which explains why it seems to be everywhere:
TL;DR: This のだ is used when an effect has been observed, and someone is asking what the cause is, or stating what the cause is.
We do this all the time in English, but we don’t have a specific grammar for it like Japanese does with のだ.