Zone offense requires that each offensive player maintains a set offensive position. A typical configuration is 3-2-1-1: three handlers, two middle cutters, a middle-deep cutter, and a deep receiver.
Another typical configuration is 3-3-1: 3 handlers (dump + 2 swings, one on either side of the dump), 3 mids or "poppers", and one deep.
An advantage of zone O is that each player is actively coordinating their movements with the thrower and each other. To contrast, where players in a stack may find themselves waiting for a proper moment to execute a cut, zone players can usually provide a constant flow of opportunities for the thrower.
In zone offense, the handlers are primarily responsible for the management of the disc throughout the attack. When a middle (or other) receiver catches the disc, the handlers move up to the line of possession, and the reciever--now thrower--dumps the disc back to a handler and moves downfield in coordination with the other recievers to set up a new flow.
The roles of the offensive players depend on the tactics of the defense.
Against a zone defense, the middles act as poppers and the job of the handlers is to wear out the defensive zone by moving the play from one side of the field to the other, at the same time looking for opportunities to advance the disc.
Where a zone offense is faced with a man-to-man defense, the receivers are free to arrange a pattern of cuts in the open field.