Hi Dan!
"Quite" is an expressive word, used to describe varying degrees of something.
In some sentences, it means "very." i.e. "I'm quite cold."
In other sentences, it means "absolutely/entirely." i.e. "I couldn't quite do stuff."
Another degree described by "quite" is "fairly/moderately/somewhat". But this might be more common in the UK; I'm not sure. In the US, we almost exclusively use "quite" to mean "very" or "entirely".
To answer your question specifically... in your sentence, "quite" means "entirely". Try replacing the word to see: "I couldn't entirely do stuff."
We use this phrase to say that we could almost do something, but not entirely. For example, if I were attempting to do a chin up, I might get halfway. Then I would tell people, "I couldn't quite do it."