Antimatter is composed of fundamental particles that have the opposite electric charge and quantum spin as those of matter.
Matter, and therefore everything seen, is made out of fundamental particles of nature. These fundamental particles are hadrons and leptons, the hadrons being further subdivided into baryons and mesons. Hadrons include the proton and neutron and leptons include the electron, muon and tau as well as the corresponding neutrinos. For simplicity, the overwhelming majority of matter in the universe is comprised of protons, neutrons and electrons. Antimatter is matter formed from antiparticles, which have the same mass but opposite charge and quantum spin to their corresponding particles. When antimatter is brought into contact with normal matter, both particles are destroyed, resulting in an explosion that is, in terms of mass to explosive power, the most powerful known to mankind.
In the late 19 and early 20th century antimatter had been the cause of much speculation within the scientific community, With William Hicks, Karl Pearson and Arthur Schuster discussing the idea. The current theory of antimatter was set down in a paper by Paul Dirac in 1928, when he realized his version of the schrödinger wave equation for electrons also raised the possibility for the existence of anti-electrons, electrons that had the same mass but opposite charge and spin. Naturally all the other particles of matter would also have their opposites.
The anti-electron was first observed by Dmitri Skobeltsyn in 1929, using a wilson cloud chamber, and again by Chung-Yao Chao in the same year. But they were first discovered (meaning in this case observed and labeled) by Carl Anderson when he separated the electrons from other types of high energy particles present in cosmic rays based on there mass-to-charge ratio. He found some particles with the same ratio as electrons that moved in the opposite direction when under the influence of a magnet. He had found the anti-electron, which he called the positron.
The anti-proton was first discovered in 1955, by physicists Emilio Segrè and Owen Chamberlain. The first anti-neutron was discovered shortly thereafter in 1956, by Bruce Cork.
Antimatter is made in supercolliders such as CERN, by smashing beams of highly charged particles together. This results in pair production, the creation of a particle and its antiparticle. One of the aims of modern physics is the creation of larger and more complex forms of antimatter. In 1995 CERN announced that it had produced 9 hydrogen atoms. In 2003 Antihelium was created. Physicists are now working on the creation of 'cooler' antiatoms, as the ones produced so far are more energetic than atoms on the surface of the sun, and this makes the extremely hard to study. Another issue being studied is that of containment: since antimatter explodes on contact with normal matter, it is difficult to hold it for study. Smaller particles are held in place by carefully managed magnetic fields, but the larger antiatoms, being magnetically neutral, are much harder to contain.
Antimatter is naturally produced by both (β+) decay and by high energy collisions between particles. Antimatter makes up a very small percentage of cosmic rays, and is occasionally produced when those rays collide with the earth's atmosphere. Antimatter has also been spotted in the Van Allen belts and forming above thunderstorms.
Potassium 40 will (very) occasionally undergo beta decay, producing an antielectron. As such, the average banana (rich in potassium) will produce a small particle of antimatter every 75 minutes.