MEDUSA is a ground-based weapon. It is stated in Mortal Engines as taking up the whole of the inside of St Paul's Cathedral, where the Guild of Engineers had rebuilt it. It is described as having a huge, metallic hood shaped like a cobra's hood. It fires a beam of energy (either sourced from outside the real universe, or the cities generators), resembling a "cat-o-nine-tails", at targets up to two hundred miles away. The coordinates are input via a control panel at the base of the firing mechanism. MEDUSA was accidently destroyed by Katherine Valentine who was mortally wounded while attempting to sabotage it. This prevented MEDUSA from firing, but caused it to overload, destroying London.
MEDUSA was used in America during the Sixty Minute War
Thousands of years after the War, London secretly made archiological expeditions to the Dead Continent and gathered the pieces of MEDUSA from an old Brothal base and re-assembled it inside St Paul's. In order to obtain the computer control system, a fabulously complex piece of technology even by the ancients standards, Thaddeus Valentine killed Hester's parents and scarred her face for life.
Katherine Valentine spends most of the first part of Mortal Engines trying to figure out what MEDUSA is. Then, when they are being chased by the city Panzerstadt-Bayreuth the roof of St Paul's Cathedral lifts up and destroys the predator with a blast of pure energy. Katherine is horrified, but the rest of London was happy that they avoided being eaten.
London then heads onwards towards Batmunkh Gompa with plans to destroy the Shield-Wall and make Central Asia their new hunting ground. Magnus Crome planned to use MEDUSA to become the greatest traction city in the world; if a city didn't deliberately drive into London's mouth then they would unleash MEDUSA on it and eat it's remains. Then when all the Traction Cities were gone they would turn the entire Earth into a planet that ate other planets.
However, they cannot complete this plan as MEDUSA overloads with energy and explodes, obliterating most of London with it.