In a conventional band, the Rhythm Guitarist is the person who plays the chords which provide the backing sound for the song. This is in contrast to the Lead guitar, which is generally the person who plays those wicked sweet solos and such.
A good rhythm guitarist should be good at keeping time and have good chord fingering techniques. In a rock band, this person is very important as they are usually the one who creates the melody for the whole song. A good understanding of complex rhythm and at least basic-level music theory are crucial to be good at this.