Antimatter is a material composed of antiparticles, which have the same mass as particles of ordinary matter but opposite charges, as well as other particle properties such as lepton and baryon numbers.
Antiparticles were first predicted in 1928, by the British physicist Paul Dirac. Dirac was one of the pioneers of quantum field theory- the theory that combines quantum mechanics with Einstein's special theory of relativity. Dirac was looking for an equation that would describe the properties of an electron, moving at relativistic speed. He managed to write such an equation, which won him the Nobel Prize in 1933. When looking at this equation, he found something strange. Just as the equation x2=4 can have two possible solutions (x=2 or x=-2), so Dirac's equation could have two solutions, one for an electron with positive energy, and one for an electron with negative energy. But classical physics (and common sense) dictated that the energy of a particle must always be a positive number.
Dirac interpreted the equation to mean that for every particle there exists a corresponding antiparticle, exactly matching the particle but with opposite charge. For the electron there should be an "antielectron", for example, identical in every way but with a positive electric charge. (In fact, initially Dirac thought that the anti-electron is the proton, but he soon realized that this cannot be, since they do not have the same mass). The anti-electron, also known as positron, was discovered in 1932, not so long after Dirac's initial prediction, by Anderson who looked at cosmic rays.
Anti-particles have all the properties of particles: elementary anti-particles can form anti-atoms, anti-molecules, and as far as we know, there could be entire galaxies and universes made of anti-matter.
However, when an anti-particle collides with a particle, they both annihilate - giving rise to variable proportions of intense photons (gamma rays), neutrinos, and less massive particle-antiparticle pairs. The total consequence of annihilation is a release of energy available for work, proportional to the total matter and antimatter mass, in accord with the mass-energy equivalence equation, E = mc2.
Thus, in fact, one of the greatest mysteries of modern physics today, is why the universe that we see is filled with particles, rather than equal amount of particles and anti-particles? The process by which this inequality between particles and antiparticles developed, which much have occurred very close to the big-bang is called baryogenesis.