A character that the audience/listeners can relate to. Something tragic happens to this character. the audience should wish it not to, despite how many times hearing/seeing the story. The character is considered a hero because they stand for a trait we all wish to have or believe in. Things like: the American Dream, the idea that if Americans work hard they will succeed in life, is a common ideal for the tragic hero to have.

It is important that the tragic hero is sympathetic. This way the listeners will be able to completely relate to the character. If there is no sympathy between a tragic hero and the listeners than the character becomes pathetic. When this happens a tragic hero is no longer tragic, just some person that had bad luck for no real reason.

The reason to have a tragic hero is to give a story purpose. A tragedy by nature isn't an uplifting story. But with a tragic hero you can learn from a tragedy. Tragic heros make tragedies worth participating in.

Some of the more interesting literary debates have been whether a particular character is indeed tragic.
Example of tragic heroes are:
Willie Loman in Death of a Salesman by Arthur Miller
Hamlet in Hamlet by William Shakespeare
I would even say that Sid Vicious in Sid and Nancy is a tragic hero.