From the mission’s website:
Gravity Probe B is the relativity gyroscope experiment being developed by NASA and Stanford University to test two extraordinary, unverified predictions of Albert Einstein’s general theory of relativity.
The experiment will check, very precisely, tiny changes in the direction of spin of four gyroscopes contained in an Earth satellite orbiting at 400-mile altitude directly over the poles. So free are the gyroscopes from disturbance that they will provide an almost perfect space-time reference system. They will measure how space and time are warped by the presence of the Earth, and, more profoundly, how the Earth’s rotation drags space-time around with it. These effects, though small for the Earth, have far-reaching implications for the nature of matter and the structure of the Universe.
Gravity Probe B is among the most thoroughly researched programs ever undertaken by NASA. This is the story of a scientific quest in which physicists and engineers have collaborated closely over many years. Inspired by their quest, they have invented a whole range of new technologies — technologies that are already enlivening other branches of science and engineering.