Actually our auction was slightly different, but carried the same effective meaning. Partner had shown a 14-16 NT with 4 spades. We had actually shown 4+ diamonds along the way. (which may affect your decision to invite later on)
You're playing in an important team match and you know the NS pair in the other room is playing a strong club system. Thus, if partner has a 16 count, then they will surely be in slam. If he has a 14 or 15 count, then they might stop short.
You have two balanced hands opposite each other and they generally won't play that well. So do you:
Bid 3NT to play and hope that it's the right spot and perhaps you can gain imps if the other room gets too high?
Bid 4NT to invite partner to the slam if he's maximum. The idea being if partner has a 16 count, then we will likely be matching the result in the other room.
Bid 6NT because we are feeling frisky and besides we are looking at a combined 31-33 hcp!

Help

1NT(14-16) - 2♣
2♠ - ?