Let's talk about Jacoby 2NT. Suppose your partner opens a major, and you have an opening hand yourself. Great! You want to play at least game, and maybe more. Suppose you have 4 cards in your partner's suit as well. Fantastic! You know you want to play in four of the major. But, with a good hand and a good trump fit you certainly want to see if slam might make. After all, if the hands do mesh together well you can make slam with fewer than 33 combined high card points. What you need is good distribution.
This is exactly the situation for splinter bids and Jacoby 2NT.
A splinter bid is a double jump shift. For example: 1S-4C, or 1H-3S. This bid shows 4 card trump support, and an opening bid, AND a singleton or void in the suit you just bid. So 1S-4C guarantees 4 spades, and no more than one club. You are showing your distribution, hoping partner can reevaluate his/her hand better as a result.
Jacoby 2NT fills a slightly different need. You still promise 4 card support, and 13+ points (some people cap it at 16 hcp), but now you are showing a fairly balanced hand. You are saying to partner, "We know our trump suit. We are going to game. We need to figure out whether our meshed distributions can bump our point count into the slam area. Please tell me if you have a short suit." The opening bidder does just that. If you have a singleton or a void, bid that suit at the lowest level over 2NT. If you don't, and you have a minimum hand, given that you opened (say 13-15hcp), just bid 4 of your major. If you have a maximum, bid 3 of your major to leave more space for exploration if needed.
Here's a hand where Jacoby 2NT was used to good effect. This is a hand I played with Jonathan in Pittsfield on Sept. 20th.
For some reason, North decided not to preempt. I opened 1S, planning to bid hearts next. Jonathan had other ideas however. With a strong hand, and a 9 card heart suit, he knew we should be in game, and slam was possible if I had the correct hand (for example, a singleton heart, the ace of diamonds, king of clubs and the AK of spades-only 14hcp). He bid 2NT, fixing spades as trump, and asking if I had shortness. I did, and showed it by bidding 3D. Now Jonathan reevaluates. His KJ of diamonds are no longer useful cards. They duplicate the singleton I have. If we count points for both the singleton and the KJ of diamonds between us, we are over-counting (just as you don't want to count 5 points for a singleton K in your hand). We his new evaluation, he knew slam was highly unlikely, so he signed off with 4S.
This was the ideal location. I played 4S, making 6 when north opted not to cash her AD when she won the AS. Maybe she should have cashed out, but cashing that A sets up the K for a possibly helpful discard, and she has no idea that my hearts are so good, so I am certainly sympathetic. Scoring 480 for 4H+2 was a tie for top, and 4.5 matchpoints.
What if my singleton were in hearts however? Then Jonathan would be excited. He could bid 4C as a cue bid, showing control there, and hoping I could bid 4D. If I could, then we are on our way to a possible slam with only 27hcp or so. And we will likely make.
Jacoby 2NT is a tool to help you evaluate how your hands fit together beyond the simple point counts use it wisely, and it will serve you well.
Some notes about use:
Jacoby 2NT is an alertable bid. That means that in real life, if your partner bids it, you say "Alert" or place the "Alert" card on the table. Do not explain unless you are asked.
There are of course variants that you could play as a follow up. In particular, the 3NT bid over 2NT is unused in my system above. You could play that as a balanced hand, or simply a medium range opener (that's probably best). Another thing you could add is a jump with a max and a void. Just make sure you discuss with your partner before you start play so that you understand each other.