The beta itself starts on February 19 (or the 18th for Xbox One users) and ends on February 21. It lets you explore all the major game modes that The Division will have to offer when it releases on March 8th. This includes a few main and side missions, along with the Dark Zone, an area that is a mix of both PvE and PvP.
Compared to the closed beta, the open beta offers a new story mission. In addition, Ubisoft claims that they have fixed some of the more blatant exploits and cheats that plagued the Dark Zone. Presumably, this means that you will probably not encounter any invisible players with infinite ammo – but being a beta, anything is possible.
Anyone who participates in the open beta will also receive an exclusive in-game reward for when The Division actually launches in March. All players will also be starting fresh in the open beta, meaning that all of your progress from the closed beta (if you participated in it) will not be transferred. In the same vein, everything that you do in the open beta will not transfer over to the full game.