I don’t agree with the ranking of quite and very in the accepted answer. The basic meaning of quite is “totally or completely”. to an extreme : positively quite

sure—often used as an intensifier with a,

quite a swell guy quite a beauty 3 : to a considerable extent : rather quite near.

The Oxford On-Line Dictionary has a similar definition:

1 To the utmost extent or degree; absolutely.

Is it true that all computers are different? 1 US Very; really (used as an intensifier)

2 Or, to a certain or fairly significant extent or degree; fairly.

Because we are just dealing with nuance rather than meaning, I would add that very is so overused that often it doesn’t intensify to a (very) great degree.