The key point was that Kennedy challenged Nixon to a series of televised debates. It was the first televised presidential debate in American history.
In 1960, 88 % of American homes had television. About 2/3 of the electorate watched the first debate on TV. Nixon was recovering from a knee injury, he looked drained. Kennedy, meanwhile, had been resting in a hotel for an entire weekend, he looked tan and confident.
Most Americans watching the debates voted for Kennedy, most radio listeners seemed to give the edge to Nixon.