Counter is term for spells that have counterpart spell which dispels (cancels) it, and which it dispels. This means that both counter spells in a pair can not be active on the same unit at the same time. When a counter spell is cast on a unit which is under the effects of its counterpart, the existing spell effect will be removed and the newly cast spell will take effect.
List of true counter spells:
List of spells with opposite effects: (these spells do not dispel each other, but their effects are equal and opposite, so they do cancel each other out)