a real world point of view
The 2nd assistant director — sometimes the 2nd AD or the second —is the chief assistant to the 1st assistant director. He or she is chiefly responsible for the maintenance of the call sheet and for looking after the principal cast.
In the performance of the first of these duties, the second must liaise with the production office, particularly the production secretary, who passes the list onto the production office, usually to the production co-ordinator, for approval. Once approved, the secretary finalises copies of the list. The second then physically provides the cast and crew with these copies, so that everyone involved with a day's shoot knows when and where they're supposed to be. Though it may seem trivial, this action is absolutely vital to the first's chief goal of keeping principal photography moving according the shooting schedule.
As filming progresses on any particular day, the second is busy actually getting the principal actors in place at the appropriate time. This can be a complex matter of organisation, as the second must correctly allow for the time other departments — such as wardrobe and make-up — will take in preparing actors for filming. If on location, the second has the additional worry of allowing time for the physical transport of actors from their overnight accommodations.
Another vital interaction the second has with the principal cast is in the provision of daily shooting scripts to the cast and crew. These "mini-scripts" will usually only be a few sides long, covering only what is being shot that day. They will have any last-minute changes made by the writing staff to the master shooting script the actors would have received around the time of the initial read-through. As with the call sheet, the second will have to liaise carefully with the production secretary (in this capacity technically known as the script secretary) to actually get the scripts for delivery.
BBC Wales productions have almost always enjoyed the presence of a 3rd AD, who principally deals with extras. In the special case of the 1996 tele-film with Paul McGann, where there was no third, second David Klohn would have also had to oversee the extras, as well, and otherwise assume the general responsibilities of the third.