Final answer:
Students wore peace armbands to protest the Vietnam War, and this action was part of a larger antiwar movement involving student organizations like the Students for a Democratic Society (SDS), ultimately leading to a significant Supreme Court case on First Amendment rights.
Step-by-step explanation:
The students wore the peace armbands to protest the Vietnam War. In December 1965, inspired by the antiwar sentiment that was growing among various student groups and organizations, students in Des Moines, Iowa, wore black armbands as a symbol of protest and support for a truce in the Vietnam war. This was part of a larger movement against the war where many student organizations, including the prominent organization Students for a Democratic Society (SDS), were actively involved in organizing protests and demonstrations. The act of wearing the armbands led to a significant Supreme Court case regarding First Amendment rights, where the Court ruled that the prohibition against wearing armbands in public school as a form of protest violated the students' freedom of speech protections.