Teams have to ability to release two players at any time prior to June 1 with a "June 1st" designation, meaning the team get June 1 release Cap treatment, even though the player is released prior to that. Until June 1, the team still has to carry the player on their Cap (even if he signs elsewhere), so there's really no Cap advantage to the team.
The reason it was added to the CBA back in 2006 was to help the players, so that they can hit the FA market when all the money is still there, as opposed to after June 1, when a lot of teams are already tapped out or have already filled their needs.