A rebellious person likes to challenge authority and break the rules every now and then. A really rebellious group tries to overthrow the government.
Being rebellious is part of the American character. If the colonies hadn't been rebellious enough to rebel against England, there would be no United States. Large groups of people can be rebellious, but so can individuals. A student who talks back to the teacher is being rebellious. An employee who ignores a dress code is being rebellious. Anywhere there's an authority, someone is probably acting rebellious toward it.