A player that is designated for assignment is removed from his club’s 40-man roster and, within the next 10 days, traded, released or, if he clears outright waivers, assigned to the minor leagues. A club may not designate a player for assignment if the corresponding transaction is to recall a player on optional assignment. Here are the options a club has in some more detail:
Trade: A club interested in acquiring a player who has been designated for assignment may try to work out a trade before the player is placed on waivers, eliminating the possibility he might be claimed by a club with a higher waiver claim priority. Players with "10 and 5 rights" may not be traded without their consent.
Release: The player then becomes a free agent. He may sign with any club, including the team that released him.
Waivers: A club wishing to send a player designated for assignment to the minor leagues must first place him on irrevocable outright waivers, making him available to the other 29 clubs in reverse order of won-lost record.
In other words, a club DFA's a player to give themselves some options. The biggest benefit to a team when a player is DFA'd, the club gets to fill his 40 man roster slot while not committing yet to a formal course of action with the player. Note that of the ten day period, the player must be placed on waivers before seven days have passed if the team wishes to go that route.