Background
The case rested on an act which most Americans would find offensive: the burning of the American Flag. Gregory Lee Johnson was arrested and tried in the Texas courts. He was found guilt of destroying a venerated object.
He took his case to the supreme court and argued that his was a form of symbolic free speech. In a 5-4 decision the court agreed with him and they overturned the Texas ruling.
They argued that the act was repulsive, but that alone did not constitute blocking his right to disagree with what the governments were doing. The descending 4 argued that Texas had every right to classify the flag as a venerated object.
The case helped insure that the 1st amendment was protected. The court ruled that individual free speech must be protected.