While we may disagree with certain points (and the general argument) of this article by Henry Siegman in a recent issue of The Nation, he nonetheless offers a very clear and useful definition of apartheid:
Olmert was mistaken in one respect, for he said Israel would turn into an apartheid state when the Arab population in Greater Israel outnumbers the Jewish population. But the relative size of the populations is not the decisive factor in such a transition. Rather, the turning point comes when a state denies national self-determination to a part of its population–even one that is in the minority–to which it has also denied the rights of citizenship.
When a state’s denial of the individual and national rights of a large part of its population becomes permanent, it ceases to be a democracy. When the reason for that double disenfranchisement is that population’s ethnic and religious identity, the state is practicing a form of apartheid, or racism, not much different from the one that characterized South Africa from 1948 to 1994. The democratic dispensation that Israel provides for its mostly Jewish citizens cannot hide its changed character. By definition, democracy reserved for privileged citizens–while all others are kept behind checkpoints, barbed-wire fences and separation walls commanded by the Israeli army–is not democracy but its opposite.