The use of 4NT, usually as a direct raise of no-trumps, to request partner to pass or bid 6NT depending on whether he is minimum or maximum in the context of the previous bidding.
If neither partner has a long suit, you will need to able to envisage 31-34 points between the two hands for a quantitative 4NT.
If partner shows a balanced 12-14 (for example by opening a weak 1NT), you make a quantitative raise to 4NT.
With the first hand, partner is minimum and passes 4NT. The second hand has 14 points (maximum) and warrants an advance to 6NT, which is a good contract.