When you respond 1NT to your partner's 1H or 1S opening bid, you will usually be denying 3-card support. You may even be void in your partner's suit, but not strong enough to change the suit at the 2-level (for which, with a void in your partner's suit, you require 10pts+). At the moment, the hand looks like a mis-fit, and you must keep the bidding low.
However, sometimes your partner will re-bid a second suit for which you have 4-card support. Now, the shortage you hold in your partner's first suit isn't such a negative feature and you can re-evelauate you hand.
If partner opens 1S, you would respond 1NT.
If partner now bids 2H, your hand improves dramatically and, although opener may still hold a minimum hand, you should raise to 3H. With 16pts+ (or appropriate distribution, such as 5-5, 6-4 or 6-5) partner will bid game. This will have a decent chance of success since you have a 4-4 fit and a long suit (opener's original 5 or 6-card suit) to establish.
NOTE to the defenders: when your opponents play in a second suit that has been agreed, and especially after 1NT in sequences such as the one described, it is almost always a 4-4 fit. Therfeore, without a stand-out lead of your own (AK or a singelton) lead a trump. You will cut out cross-ruffing opportunites on which the declarer may be relying.