What I was taught
I was taught that the んです form in statements (not questions) emphasized the preceding predicate as shared information. My interpretation of this is that when you're using んです to make a statement, you're acknowledging that the person you're talking to is in a group for which the information is appropriate.
This can be subtle. A particular example the teacher mentioned was an upper level student commenting to her that the new students were quite good this year. But since he used the んです construction, she felt slightly insulted. In this case, it wasn't shared information. As the teacher, it was her information.
In the case of yes/no questions, this variation implies that the statement is true, and you're just verifying it.
In the case of non-yes/no questions, the construction can be seen as emphasizing the "concreteness" of the question.
My rough translation: "It is [the case] that"
My personal interpretation, that has worked fairly well for me, is to interpret it as some variation on the phrase "it is that".
In statements, "it is the case that..." can carry roughly the same nuance, although that may just be my personal speech pattern in English.
In yes/no questions, "Is it the case that..." works fairly well as a reflection of both the heightened formality and increasing concreteness.
In non-binary questions, "is it that" often works, "itsu tsukimashita" (When did X arrive?) becomes (When is it that X arrived?). "Who joined?" -> "Who is it that joined?".
EDIT: Modified a few things and clarified that one of my statements was at best a guess.