After a 1NT or 2NT opening bid, 2♣ or 3♣ asks partner to bid a five-card major. The diamond response (2♦ or 3♦) denies the holding. If responder has a four-card major, he bids it on the second round and opener will confirm a 4-4 major suit fit if one exists.
In the UK, while it is quite common to play five-card Stayman in response to 2NT, few pairs use it in response to 1NT.
Here is an example of the convention in action: