Biphasic sleep is a routine of sleeping for two periods (bi-phasic) instead of one traditionally done in the evening (monophasic). This is a variation on polyphasic sleep.
Biphasic sleepers time their sleep schedule to maximize their amount of REM sleep. Most individuals complete a REM cycle in 70-90 minutes. By waking up at the end of a cycle you don't try to pull your brain out of a deep sleep thus a more restful experience sometimes including more vivid dreams.
An example of a biphasic schedule would be sleeping from 8:30 pm to 10:00 pm (90 minute cycle), and then from 1:30am or 3:00am to 6:00am (3 or 4 cycles).