Translation:I cleaned up my house yesterday.
Something like that. ～んです is a hard one to explain (not least because I only learned about it conversationally), but generally speaking, I think it's a way for adding emphasis. What is being emphasized is entirely dependent on context though... For example, in this question:
- as an opening to a converstion, it reads kind of like "guess what, I cleaned the house yesterday, how interesting isn't that ;)"
- as a response to an interrogative question like "where were you yesterday", "well, actually I had to clean the house"
- as a response to a general question like "what did you do on the weekend", "I simply cleaned the house yesterday (as opposed to doing anything else)"
I'm sure there are other examples/possible translations that I'm not thinking of, and people will probably disagree with the exact wording of my translations, but the point is adding ～んです can change the nuance of the sentence in different ways.
At OP: as an English native speaker (Australian), simply adding "it's that" feels very stiff and unnatural in almost all cases, and it's not a good way of translating ～んです. I think it's a good way to remind yourself that ～んです is different from just です, but you should probably give it a bit more thought after that.
I think the "The 「の」 particle as explanation" part of the link might provide to be helpful to you. I hope it will.
I think an easy way to explain the んです/のです is that it's used to explain things or give reasons. This example meaning for example, would never be used alone or as a conversation starter. It's answering a question, giving an explanation.
Why are you so tired today? 昨日、家の掃除をしたんです (Well, because I cleaned my house yesterday)
Why are you late? 電車に乗り遅れたんです (You see, I missed the train)
You can add it to adjectives too:
Why aren't you eating? 寿司が嫌いなんです (Because I don't like sushi)
"To clean house" has a different meaning in English from the Japanese verb: https://www.urbandictionary.com/define.php?term=clean%20house