2k is the name given to one of the several digital cinema standards. It has 2,048 horizontal lines of resolution, and most commonly 1,556 vertical resolution, though this can depend on the aspect ratio. This is a slight increase from standard HD's 1080p, which is 1,920x1,080.
Most films shot digitally are shot at 1080p or 2k, and most digital cinemas are at best 2k.
The few films shot at the 4k digital cinema resolution are downcoverted to 2k so they can be shown in more digital theaters or transferred to 35-millimeter film.
