The groove is the feeling of a musical performance, specifically to the feeling that all of the performers are performing in rhythmical and stylistic sync with one another. When a performance or an ensemble is "in a groove," all the performers are all playing in perfect sync and the music typically has a effortless and exciting sound.
The groove may also refer to the act of performing a musical style (for example, swing or funk) on the drums that the rest of the ensemble can follow. To 'lay down a groove' means to perform a specific style in a manner that provides no doubt in the minds of the other performers as to the beat of the music, and when a performance is "in a groove," one can hear a solid rhythmic underpinning to the performance of a composition by the rhythm section.
Finally, groove may refer to rhythmic ostinato, usually distinguished by rhythmic counterpoint; i.e., not all instruments articulate all beats; instead, the rhythmic activity is distributed among the performers in complementary fashion, with all or most lines coinciding only on structurally important events.