Armstrong's famous "one small step" quote - explained

What did Neil Armstrong really say when he took his first step on the moon? Millions on Earth who listened to him on TV or radio heard this : "That's one small step for man, one giant leap for mankind."
But after returning from space, Armstrong said that wasn't what he had planned to say. He said there was a lost word in his famous one-liner from the moon: "That's one small step for 'a' man."
"The 'a' was intended," Armstrong said. "I thought I said it. I can't hear it when I listen on the radio reception here on Earth, so I'll be happy if you just put it in parentheses."