This was a landmark Supreme Court case that established the right to have an attorney appointed to you if you cannot afford one (the right to legal representation). This is a right that is given to everyone who is charged with a crime even to this day, so has had a major impact on the representation of people who could not otherwise afford representation.
Mr. Gideon was accused of burglary and was forced to represent himself because he was poor and couldn't hire a lawyer. He was convicted of the crime but fought the conviction and eventually got it reversed because he showed that his rights were violated since he was not allowed to have legal counsel to help him.