Splinters, as their name implies, means that the suit you bid contains a singleton or a void AND you have trump support.

A splinter is a double jump shift by responder, or

Any UNNECESSARY jump by either bidder in the auction.

A splinter shows a singleton or void, game-forcing values, and implies at least an 8 card trump fit.

Examples:

1S 4C* --- a double jump shift, splinter supporting S

1H 3S* --- splinter supporting H

1D 3H* --- splinter supporting D, should have 5+ diamonds, since opener ONLY promises 3.

1H 1S

4C* ---splinter supporting S, 3C would be a forcing re-bid

1D 1H

3S* ---splinter supporting H, 2S would be a forcing re-bid

1H 2C

3D* ---splinter supporting C, remember 2/1 is game forcing, so there is no need to jump to

1C 1H

1S 3D* ---2D would have been forcing (a new suit after a suit rebid always is), so 3D is a splinter in

1C 1H

1S 4C* ---2C would not be forcing, 3C would be, so 4C is a splinter bid supporting S