There's a really good podcats for laypersons from Teamestry Making an Impossible Airplane: The Untold Story of Concorde that explains this briefly. Here is a summary from the Internet: Before Concorde takes-off, the flight engineer will start to move fuel from the forward trim tanks to the rear trim and collection tanks, this will continue during the acceleration through Mach 1 and onto eventual Mach 2. During this process around 20 tons of fuel is moved and this results in a shift of the CG by 6ft (2meters). This will neatly balance the change in the centre lift of the aircraft.
Also needed to move it froward for landing.
All this designed with slide rulers and the UK team in Imperial while the French team using Metric.