The throttle assembly was a component (or series of components) of the propulsion system of Earth's first warp-capable vessel, the Phoenix.
Integrated into a Titan II nuclear missile by Zefram Cochrane and his team of engineers in Bozeman, Montana in the mid-21st century, the throttle assembly utilized theta radiation. On the evening of 4 April, 2063, the Phoenix rocket was damaged in its silo by a Borg attack, launched from the 24th century. Large doses of theta radiation leaked from the damaged throttle assembly, causing severe radiation poisoning in Lily Sloane, a member of Cochrane's team.
The throttle assembly was ultimately repaired and the Phoenix flew on the following day, 5 April, 2063. (Star Trek: First Contact)
The specific function of the throttle assembly was never stated on screen, however, it is likely that it served to regulate the power in Cochrane's warp engine, much in the same way a throttle regulates air flow in the internal combustion engine of an automobile.