A very posh expression used to express profound agreement, with strong understatement. Only used by the highly posh British. The 'double-quite' is a relative of the 'single quite', used in the similar circumstances, but less profound and much more common. The double-quite is not to be used by amateurs, or the would-be posh. It confers an added degree of standoffishness, unexpressed opinion or derision (as compared to the single quite) with respect to the person or thing being discussed.
person1: if Anne Boleyn doesn't give the king a male heir, she's going to be in trouble!
person 2: quite, quite