No, antimatter is quite physical--just really, really scarce. (This scarcity is a puzzle in itself, but lucky in that contact between normal matter and antimatter results in conversion of both into energy--that is, mutual annihilation. It would be inconvenient for us if this happened often--especially since the energy released is very large.)
But getting back to the question of what antimatter is, it is simply matter composed of particles possessing the reverse charge and magnetic moment to normal matter. For example, a normal electron has a negative charge; an 'antimatter electron' has a positive charge (which is why it's sometimes called a positron.)
The positron was the first antiparticle to be observed; at present science has been able to construct antimatter as large as antihelium.