The Vietnam War was one in which thousands of 18 year old American males were drafted into military service. Many citizens felt that it was unfair that these citizens who were forced to serve, did not have a chance to vote for the President, Congress, or any elected office.
Along with this, many college campuses protested the US involvement in Vietnam. This was one of the only ways they could show their dissatisfaction with the American government, as many of them could not vote.
Based on the aforementioned facts, the 26th amendment was passed. This gave 18 year old citizens the right to vote in federal elections.