In the old days, you had to be half-human, half-god to be a hero, like Hercules, Theseus and Perseus.
When the gods were no longer fashionable, heroism came to be defined by the acts of defeating danger or rising above adversity to achieve the greater good. A hero was defined by courage, self-sacrifice and doing the right thing like King Arthur and Sir Galahad did.
Some heroes go on journeys; from the ordinary world they heed the call of adventure, crossing over into an extraordinary realm full of trials and challenges, which, once completed, change the hero but not the ordinary world they return to; Luke Skywalker and Bilbo Baggins are examples of a heroes who went on a journey.
Other heroes appear and act more like villains---they lie, cheat, steal, fight unfairly, even walk away---yet unexpectedly stand up for the downtrodden and play the role of the protector, like Wolverine, the antihero.
Nowadays, a hero can simply be an ordinary person in an extraordinary situation, prevailing despite the odds stacked against them, like the people featured on the website MyHero.com.