"Quite a while" means "a pretty long time". It's not a really long time, but it's also not a short length of time.
Exactly how long "quite a while" means depends on the situation. It can mean minutes, days, or even millions of years.
A: How long did you have to wait for?
B: Quite a while.
I haven't seen her in quite a while. What's she been up to?