The idea is called "civil disobedience". It was named by Henry David Thoreau in the 1840s, but the basic concept has a long and distinguished history that goes back many centuries before that; similar ideas of a "law above the laws of man" are discussed in some of the earliest documents on record.
In civil disobedience, people who believe that a law is unjust intentionally, publicly, and nonviolently break that law. Typically this is done with a group of people working together, but it can be done by an individual alone. They then accept their punishment for doing so, but seek to draw public attention to the injustice of the punishment in order to undermine the unjust law.
For example, Mahatma Gandhi was well-known for using civil disobedience on a number of laws that discriminated against Indians in South Africa as well as laws put in place by the British over India. In the 1960s, Martin Luther King Jr. (whose national holiday was celebrated yesterday!) engaged in civil disobedience against racial segregation laws in the United States.
There are two important features of civil disobedience to note, which many people misunderstand:
1. It is by definition nonviolent. Civil disobedience does not mean rioting or fomenting revolution. It means peacefully and publicly challenging laws you believe are unjust.
2. It does not excuse you from being punished. Most governments worldwide do not accept any kind of "civil disobedience exception" that would protect people from being punished if they break laws they deem unjust. You are still expected to obey all laws, and if you don't you are punished accordingly. Part of why civil disobedience is so difficult and courageous is that it often involves spending time in prison as punishment for the laws you have broken.