Outside of the competitive scene, monotype teams are used purely for the novelty of it. There's no benefit to using a team like this. Some might like it as an added challenge or as an alternate way to the play the game, but there's really no reason to limit yourself to one type if your main concern is playing and winning the game normally.
Within the competitive scene, however, there is a monotype metagame run by Smogon that is fairly popular. It uses a similar set of rules to standard OU, but has its own banlist and of course, the requirement that all Pokemon on the team have a type in common. Monotype teams are generally used for play in this metagame, which is played primarily on Pokemon Showdown. Apart from this, monotype teams have little use or application in the competitive game, as they limit too many teambuiling options to be useful, and obviously make team synergy more difficult.