One thing he did was normalize presidents putting themselves out in the public. He was the first president that sat down in front of the camera and addressed the American people more regularly. Nowadays, presidents like Obama do it because of JFK normalizing it.
His assassination also brought the American people together through nationalism. Americans felt more connected to one another as, "Where were you when JFK got shot?" became a normal icebreaker question. This could be said for 9/11 as well.