As the GRACE-twins fly in formation over the Earth the precise speed of each satellite and the distance between them is constantly communicated via a microwave K-band ranging instrument. As the gravitational field changes beneath the satellites - correlating to changes in mass (topography) of the surface beneath - the orbital motion of each satellite is changed. This change in orbital motion causes the distance between the satellites to expand or contract and can be measured using the K-band instrument. From this, the fluctuations in the Earth's gravitational field can be determined.
Here's an example of how it works. The two GRACE satellites are traveling in space, both 500 kilometers above the earth. As the front satellite approaches an area of higher gravity, it will be pulled toward the area of higher gravity and speed up. This increases the distance betweenthe two satellites. As the satellites straddle the area of higher gravity, the front satellite will slow down and the trailing satellite will speed up. As the trailing satellite passes the area of higher gravity, it will slow down and the lead satellite will not be affected. As the satellites move around the Earth, the speeding up and slowing down of the satellites will allow scientists to measure the distance between the two satellites, and, therefore, map the earth's gravity field.A map of the Earth's gravitational field can in turn be used to infer mass changes driven by (for example) melting glaciers, changes in groundwater, or a variety of other phenomena, making GRACE useful for a wide variety of different research topics.
JPL's main site for the project is here, and a (long) list of publications using GRACE data is available here.