This is the 36th most frequent Korean word.
게
The Korean word "게" can mean "crab" or function as a grammatical particle meaning "what/how" depending on context.
In this sentence, "게" is a casual abbreviation of "것이", meaning "what" or "thing that."
이건 내가 한 게 맞아.
This is indeed what I did.
Here, "게" is derived from "것이", which can introduce a subordinate clause or statement of fact.
비 오는 날엔 기분이 좀 우울한 게 사실이야.
It's true that I feel a bit down on rainy days.
In this usage, "게" acts as a nominalizer similar to "것이", turning a phrase in the preceding sentence into a noun phrase.