のだ (んだ, のです, んです, or の) seems to create an information deficit. There was an article written by Derek Schaab about this.
The の here is called a formal noun. It is very often translated to "It is that~", "the case", "the situation" or "the fact". When used to end a sentence, it may imply that it is an explanation to some previous context (filling up the information deficit). When used to ask a question it begs a deeper explanation over a superficial reply (creating an information deficit).
Consider:
私は猫が好きだ - I like cats
私は猫が好きなのです。 - It is that I like cats
For 1, it is a neutral statement that just says that you like cats.
For 2, it fills in a blank with the fact that you like cats as some sort of explanation. For example, if you got distracted by a cat and went out of your way to pet the cat, and your friend who was with you at the time gave you a quizzical look. You may reply 私は猫が好きなのです。 as an explanation to your behaviour to fill in the information deficit of your friend.
You can also use のです to immediately fill in an information deficit that you think the listener should have:
- 今日は出かけられない。宿題がたくさんあるのです。 - "I cannot go out today. (The reason being that) I have lots of homework.
のです can also be used when no information is shared by the speaker and listener, and is not used to express reason or an explanation. When used as such, the speaker speaks as though the information was shared and the effect this creates is to involve the listener in what the speaker is talking about, or to create an emphasis on what the speaker is talking about (by means of creating a perception of information deficit of the listener).
(heefske has done a better job of explaining this in another question the summary is that it builds rapport by showing emotional investment in the issue.)
Usage pattern:
Verb
+ のです
するのです - it is that ~ is/will be done
Verb(past)
+ のです
したのです - it is that ~ was done
い-Adjective
+ のです
高いのです - it is that it is expensive
い-Adjective(past)
+ のです
高かったのです - it is that it was expensive
Noun
+ な(attributive だ)
+ のです
猫なのです - it is that it is a cat
Noun
+ だった(past だ)
+ のです
猫だったのです - it is that it was a cat
Noun(adjective)
+ な(attributive だ)
+ のです
静かなのです - it is that it is quiet
Noun(adjective)
+ だった(past だ)
+ のです
静かだったのです - it is that it was quiet