The Jacoby 2NT convention is a game-forcing response to a 1 or 1 opening bid. The 2NT response shows 4+ trump support with 13+ points (Playing 4 card Majors, with 5 card majors shows 3 card support). It also denies a void or singleton, otherwise a splinter bid is the better option. It asks partner to describe her hand further so that slam prospects can be judged accordingly. 

Opener's Rebids

After the auction begins 1/ : 2NT, opener's rebids are as follows.

Opener's Rebid	Meaning
3	Singleton or void in clubs.
3	Singleton or void in diamonds.
3	If  are trumps, then this rebid shows a better than opening hand and possible slam interest and 17+ points and interest in slam asks responder to describe his hand further. If  are trumps, then this shows a singleton or void in hearts.
3	If  are trumps, then this rebid shows a better than opening hand and possible slam interest and 17+ points and interest in slam asks responder to describe his hand further. If  are trumps, then this shows a singleton or void in spades.
3NT	Good 13-15 points, balanced, no singleton/void.
4	5+ clubs.
4	5+ diamonds.
4	If  are trumps this shows a minimum hand and no ambition to explore a slam. If  are trumps, then this shows 5+ hearts.
4	If  are trumps this shows a minimum hand and no ambition to explore a slam.

Responder's Rebids

• After any 3-level rebid by opener, responder can bid any suit (besides the agreed trump suit) to show a first-round control - i.e. an ace or void.
• After ANY rebid by opener, 4NT is Blackwood (or Roman Key Card Blackwood).

2NT by a passed hand

Jacoby 2NT is off when responder originally passed. In that situation, 2NT is natural and non-forcing, showing a balanced 11-12 HCP

In Competition

If the opponents intervene after the opening bid then 2NT bid has a different meaning so a cue bid of their suit is normally played as Jacoby.