There's a few reasons to do this, apart from the obvious one of potentially staying out and winning the stage:
1) As sparks says, it gets the jersey featured on the tv screens = happy sponsors. (Individual profile increased also doesn't do any harm for the individual = potentially more or better personal deals, endorsements etc)
2) Tactical probing of individual opponents - If I break, can so-and-so stay with me or catch me?
3) Tire out a rival team to help your leader e.g. your team doesn't help bring back the break, so your rival team has to do the heavy lifting to reel it back in, tiring their riders and giving an advantage to your team who have sat back and kept their legs fresh(er). Then your team can lead out your sprinter for example and claim the stage win that way.
4) Negate points for climbs and sprints - your teammate is leading, say, the king of the mountains or sprint points - a breakaway hoovers up some or all (depending on lone or group) the available intermediate sprint / climb points, protecting your team mate's lead.
5) Just for the hell of it (see Jens Voight).