Afterburning was added to Concorde for take-off to cope with weight increases that came after the initial design. It was also used to accelerate through the high-drag transonic speed range, not because the extra thrust was required, but because it was available and improved the operating economics.

Yes, the Concorde was one of the few commercial aircraft in history to utilize afterburners, or "reheat" as it was known in British terminology. The four Rolls-Royce/Snecma Olympus 593 engines used reheat during two critical phases of flight. First, it was used during takeoff to provide the massive thrust necessary to get the heavy, delta-winged aircraft off the ground; this was responsible for the Concorde's legendary deafening roar. Second, the afterburners were engaged to help the plane push through the "transonic" region (around Mach 0.95 to Mach 1.7) where aerodynamic drag is highest. Once the Concorde reached Mach 1.7 and the air became "easier" to slice through, the afterburners were turned off, and the plane performed a "supercruise" up to Mach 2.02. This was a marvel of engineering, as using afterburners for the entire flight would have consumed far too much fuel to make transatlantic journeys commercially viable.