Essentially, it allows a club to open up a roster spot while it figures out what it's going to do with a player.....
There are certain situations in which a team needs a player's permission to either trade him or send him to the minors. So rather than force the player to make a quick decision, the team can simply designate him for assignment while he decides....
More commonly, a player is designated for assignment so the club can open up his roster spot while they're waiting for him to clear waivers, which can take four or five days.