The lock case is the metal body that holds the mechanism: bolt, latch, springs, cams and the space where the cylinder goes or the levers work. In a mortice lock it sits inside the edge of the door; in a rim lock it is on show on the inside.
Its measurements are what count when a lock has to be replaced: the height and depth of the case, the position of the cylinder and the handle, and the distance between them. If the new one does not match, the door has to be altered.
When the key turns but does not move the bolt, or the handle spins loose, the fault is usually inside the case and not in the cylinder. Before changing anything, it is opened up and checked. You will find this under lock repair and lock installation.