One of the morals of the story is that you never know what you are capable of until you try. Harry was faced with extraordinary circumstances, and he was able to rise to the challenge. He found reserves of bravery within himself, as well as special abilities.
Harry Potter had no idea that he was a wizard, of course. When he was eleven years old, he found out he was a wizard and was whisked off to wizarding school. That was pretty unusual. Until then, he had no idea he was “The Boy Who Lived” or that he had famous parents.
From the beginning, Harry exhibited traits of bravery and curiosity. He saw Hagrid take something from a vault at Gringotts, and he wanted to protect it. He thought that it was Snape who was after it, and about that he was wrong, but at least he tried to protect Hogwarts. Harry made friends based on their character traits and not prestige. He discovered that he had talents he never knew he had, including an aptitude to play the sport Quidditch.
Harry risked his life to follow the Sorceror’s Stone deep into the castle to stop anyone from taking it. He thought it was Snape, but it turned out to be Quirrell. Harry was brave enough to fight off Quirrell, even though he was harboring Voldemort.
Harry jumped to his feet, caught Quirrell by the arm, and hung on as tight as he could. Quirrell screamed and tried to throw Harry off – the pain in Harry's head was building -- he couldn't see -- he could only hear Quirrell's terrible shrieks and Voldemort's yells of, "KILL HIM!... (Ch. 17)
Harry is later told by Dumbledore that he saved the stone because he wanted to rescue it, and not use it. In this way, the person who took the stone had to have good intentions. Harry had good intentions, whereas Quirrell and Voldemort did not.
You see, only one who wanted to find the Stone -- find it, but not use it -- would be able to get it, otherwise they'd just see themselves making gold or drinking Elixir of Life. (Ch. 17)
Voldemort got away, but he did not get the stone. This was directly a result of Harry’s bravery. He found that he had many traits he did not realize he had before he went off to wizarding school.