When to use 「~んです」

Q: In what kind of situation can I use 「~んです」?

A: You have learned 「~んです」, but you still might not have a deep understanding of the expression. Please consider the differences between the 2 sentences below.

1) 寒いです。

2) 寒いんです。

1) is used when you are just describing the cold, and there is no additional nuance. 

However, you can add the following nuances: 

a) explanation 

b) notice/discovery 

a)  When it's cold and you want to ask your teacher to switch off the air-con. In this case, you explain that it's cold ( 寒いんです） and ask your teacher to switch off air-con (エアコンを消してください）.

This sentence pattern is often used to make a request, because when you request something, you usually explain the situation. 

And to connect sentences when requesting for something,  「~が」is used.

So the sentence should be「先生、寒いんですが、エアコンを消してください」 

b) And 「~んです」is also used to indicate 'notice/discovery'. 

For instance, when your friend ate something and made a wry face, you thought that the food is not nice.

Then you can say 「その食べ物はおいしくないんですか」.　If you say 「その食べ物はおいしくないですか」, then that means that you have no idea whether the food is bad or not. 

But as your friend made a wry face, you can assume that it's not so nice. So it's better to say「その食べ物はおいしくないんですか」.