Sputnik
Sputnik is Russian for satellite. The Sputnik Program was the name given to the launching, by the Soviet Union, of three artificial satellites, the first to ever be launched. Sputnik I, II and III were the names given to those three satellites.
Speech Relevance
From 'Encroaching Control':
The foot in the door of education has been the $900 million National Defense Education Act of 1958. The excuse, once again, was the Cold War, Russia had put a Sputnik into the heavens, obviously something must be wrong with our education system. And so we are presented with a picture of overcrowded classrooms, of destitute teachers and of bankrupt school districts.
This assertion by Reagan is backed up by a number of sources online, including the Department of Education's own website.
The Cold War stimulated the first example of comprehensive Federal education legislation, when in 1958 Congress passed the National Defense Education Act (NDEA) in response to the Soviet launch of Sputnik. To help ensure that highly trained individuals would be available to help America compete with the Soviet Union in scientific and technical fields, the NDEA included support for loans to college students, the improvement of science, mathematics, and foreign language instruction in elementary and secondary schools, graduate fellowships, foreign language and area studies, and vocational-technical training.