Jacoby

What is Jacoby? A bid of 2NT over 1 of a major from Partner, showing a good raise in Partner's major. It should have 7 or less losers generally, unless the bid is made after an initial pass, when it could possibly have 8 losers. It will NEVER have a flat 4-3-3-3 hand with the 4 cards in Partner's Major but equally, shouldn't have a singleton or void, when you should use a splinter instead of the 2NT bid.

You Partner  
1H 2NT 2NT guarantees (if not a passed hand) 4+ hearts, and
a game force.
3C** 3S 3C is a trial bid, and asks for help in clubs - 3 small clubs will generally deny help! 3S is a very good hand, probably a cue bid in spades and will therefore offer help in the club suit
3NT 4H 3NT must be 15-19 points, otherwise, you will bid 4H. 4H is NOT a sign off, if you wanted to sign off, you wouldn't have bid 3S in the first place!
Etc.Etc 7H  

** A possible use of the 3C bid.

The hands might be:

You Partner
♠ K Q ♠ A x x
K Q 10 8 2 A J 7 5
A K 8 7 4
♣ 8 4 2 ♣ A K J 6

On these hands, you can make 7H!!

Jacoby/Trial Bid/Splinter

You Partner  
1♠ 2NT  
3♣ 4

3♣ is a trial bid, and 4 is a splinter (probably a singleton), with help in the club suit also.

Note: 1♠ .. 2NT .. 3♣ as a sequence is forcing to game, so 4 cannot meaningfully be anything but a splinter

Normal Jacoby sequences:

a) 1 2NT  
  3 4 Simply bidding game
       
b) 1 2NT  
  3♣ 4 Whatever the 3C bid meant, 4H shows a minimum, and is NOT forcing
       
c) 1 2NT  
  3♣ 3 Seeing as 2NT is forcing to game, this 3H bid must be stronger than the 4H in the above sequence. It is giving West the opportunity to make a cue bids.
     
d) 1 2NT  
  3♣ 3  
  4   The 4H bid shows no additional values, and is to play.
       
e)   Pass  
  1 2NT  
  3 Pass The 2NT bidder can pass, when he/she has already passed on the first round!