Slider break (sometimes abbreviated as SB) is the act of breaking combo by not fully completing a slider. It occurs when either the head or one of the ticks of a slider are missed.
Slider break will not be triggered if the slider's tail is skipped, or if the active key is released over a part of the slider's body devoid of slider ticks. The latter property of a slider's lenience is exploited in the 2B maps, which contain concurrent sliders and circles.
Slider breaks, by their definition, break combo, but instead of a miss, the player will receive a GOOD. As a result, it's still possible to get the S or silver S grade for a play, assuming that all other accuracy requirements have been met.