How can Supreme Court opinions later be used?

The decisions they make later apply to every similar situation everywhere in the country. For example, there was a case in which students wanted to wear armbands protesting the war, but the school said that was disruptive. The Supreme Court sided with the student, and said they had a right to free speech as long as it wasn't causing a material interruption. This case would later be the example on how to solve many cases regarding student's freedom of speech.