When things are opposed, they're against each other. Two teams playing against each other are opposed; so are two sides in a war.
If you're opposed, you're usually up against an opponent or opposing side. Politicians often talk about being opposed to one law and in favor of another. If someone is against higher taxes, they're opposed to higher taxes. Someone on the other side is opposed to lower taxes. But you could also simply be opposed to something like breakfast before 10 am.