When your partner opens 1H and you bid 1NT (forcing or semi-forcing), there are many possible shapes for your hand. You could have any hand from
AKx xx Kxxx Jxxx
x none QJxxxx KJxxxx.
So many different handtypes in this one bid... but the one thing they all have in common is that they have fewer than four spades.
So what does a later spade bid by the 1NTer mean?
If opener rebids something at the two level, a jump to 3S is a splinter raise. So, 1H - 1NT - 2D - 3S should look something like:
7 K3 AQ6432 QT53.
But how about the "simple" 2S rebid?
The way I play it, over 1H - 1NT - 2m, 2S shows a maximum raise in the minor (tending to not have spade shortness - see above). 1H - 1NT - 2C - 2S is probably something like
K63 J4 Q75 AJT83.
Playing this, I can give a "courtesy raise" to 3C with a hand like
J63 J4 T75 AJT83,
and partner will know not to take me too seriously since I didn't start with 2S.
When partner rebids 2H over my 1NT, I use 2S as a two-way bid. This shows either a three-card limit raise in hearts, or an invitational hand with 5-5 in the minors. Opener treats it as the minor hand, generally showing his preference at the three level. If he wants to accept game in a particular minor, he bids four of that minor, forcing. You still have to leave room for partner to correct back to 4H with the three-card limit raise!
The flip side of this is when the auction goes 1H - 1NT - 2H, a 3H bid shows limit-raise strength with only two cards. This information can be very helpful for close game decisions.
So let's say responder holds
(A) A8 6 KJT62 Q8532
(B) J86 KQT A963 T65
(C) 4 KJ3 AJT74 J752
in these sequences:
(1) 1H - 1NT - 2D -
(2) 1H - 1NT - 2H -
My suggested auctions:
(A1) ... 2S! [great diamond raise] - 3D [I'm not interested] - P
(A2) ... 2S! [good hand with both minors] - 3m [I choose this one, please go away] - P
(B1) ... 3H [three-card limit raise]
(B2) ... 2S! [good hand with both minors]- 3D - 3H [cancel that, I really have a great heart raise]
(C1) ... 4H [started out as a three-card limit raise, but your diamond bid made this hand a game-force]
(C2) ... 2S! [good hand with both minors] - 3D - 4H [started out as a three-card limit raise, but your diamond bid made this hand a game-force]