Antimatter is a self-explanatory term; matter opposite from "ordinary" matter (matter which we are familiar with).
Antimatter is said to be extremely rare, because when antimatter and matter meet, they completely annihilation eachother resulting in the most efficient way of transforming matter into energy. It was physicist Paul Dirac who first predicted the existence of antimatter in 1932 with the discovery of positrons.
In 1995, Switzerland scientists managed to create nine atoms of anti-hydrogen, each of which existing for a few billionths of a second before colliding with atoms of normal matter, causing the obliteration of both.
Larger batches of antimatter have been created - more than 50,000 anti-hydrogen atoms were whipped up in September 2002.
Physicists hypothesize that when the universe was first formed, an equal amount of matter and antimatter were created along with it. Of course, it would be the matter which predominates locally and antimatter which prodominates elsewhere; there could be entire galaxie with antimatter stars, nebulae, planets and even people.
Those who are avid fans of Star Trek are already familiar with antimatter, as it is used as the primary source for energy production in Starfleet propulsion systems.