In British English, 'quite' can mean both 'fairly' and 'very', often distinguishable only by intonation or the strength of the adjective.
So "it is quite wet" = it is a bit damp. But "it is quite wet" = put your wellies on.
And "it is quite nice" = it is ok. But "it is quite wonderful" = it is amazing!
Of course it can also mean "exactly", as in "quite so" or "quite right" or simply "quite" on its own.