Antimatter is material composed of antiprotons, antineutrons and positrons rather than protons, neutrons and electrons. Antimatter is like ordinary matter, but its building stones have opposite charge and spin than matter has.
When antimatter and matter collide with each other, all their mass is annihilated, i.e. totally transformed into radiation energy. Annihilation is the most effective energy transformation known to mankind.
Antimatter engines let matter and antimatter annihilate under controlled conditions. They use the radiation energy set free by annihilation to accelerate the propellant mass out of the thrusters. They are the most effective engines, often used to move heavy capital ships.
Antimatter is also used in weapons, like in antimatter warheads for rockets.