This is a timer from a German V-2 rocket. This weapon, used from 1944 on up through the end of World War II, can be considered the world's first ballistic missile. This electromechanical timer is typical of those used to control various internal operations of the rocket after launch. The unit changed the trajectory at a predetermined time from the initial straight vertical to the inclination calculated to direct the rocket to its target. A short period later a signal from the timer closed valves to shut off fuel the alcohol-liquid oxygen engine to allow the missile to coast on a ballistic course.
This timer was transferred to NASM from NASA's Marshall Space Flight Center in 1994.