The Background of Apollo 11
In the 1960s, many Americans believed they were in a "space race", fueled by JFK, to reach the moon before the Russians did. There is debate nowadays over whether there really was a race with the Russians, or whether NASA and other agencies just wanted more cash to spend. In any case, the nation gripped space travel with a fury, many TV shows played up a love of space travel (think Star Trek and Space 1999) and we got closer and closer. Our quest culminated when the Apollo 11 lander touched ground on the moon, and Neil Armstrong stepped down into the moon dust.
For the record, Neil Armstrong claims that his acutal quote was:
"That's one small step for a man,
One giant leap for mankind."
The "a" was very quiet and often lost in the microphone noise. There is still debate over what he actually said, maybe he made a mistake while saying it? That was his INTENTION, in any case.
Also, because his first step was so small and careful, later TV replays often had him saying those lines while he took his more courageous leap off the step.
Neil A. Armstrong
Edwin E. "Buzz" Aldrin, Jr.
Was the Apollo 11 moon landing a Hoax?
Astronomy Information Pages