Here's the British usage:
It depends on the category of adjective and the stress pattern.
1. If it's a gradeable adjective (good, bad, nice, big, small, pretty, expensive, frightening etc) 'quite' means 'a little' and tones down the force of the adjective. So 'quite good' means OK, reasonably good. Both words could have equal stress, or we might stress the 'quite' to emphasise the point that it's not 'very good' but just 'QUITE good' i.e not bad, but not very good either.
2. If it's an ungradeable adjective (fantastic, terrible, beautiful, terrifying), 'quite' means 'totally'. So 'quite terrible' is equivalent to 'completely terrible'. In spoken English, we would stress the adjective rather than the 'quite'. So 'quite AWFUL' would mean 'absolutely awful'.
NB American English doesn't tend to use 'quite' in the first sense.