When this is achieved the band and audience can ride on a musical journey with the music. All the flashy chops in the world don't mean a thing if there isn't a rhythmic foundation referred to as groove, time and feel. Even music that is non rhythmic or textural, such as free jazz or sonic evocations of mood or place, has a movement through time, a flow or groove and a particular feel. They are actually interdependent parts of rhythm and their meanings are intertwined around each other. This is rhythm.
Groove is basically a rhythmic pattern played in a consistent manner over time.
Time, in the musical sense, means tempo. That is, the rate at which the movement passes through time. Feel is literally playing a musical piece with the proper feeling. The feel with which it is played, however, would differ for each musical style because the feel of each is different. For groove and feel, first, play simple patterns in different styles for long periods of time.