To quote a very long entry in the FiMFiction FAQ which is currently down for revising:

Tragedy: The most confusing category by far, the Tragedy Category is often misunderstood and misused. A Tragedy has, by definition, a sad ending, but it doesn't mean the story is sad until that point; unlike a Sad story, it always, always will have a sad or bittersweet ending.

In a Tragedy, the heroine fights through amazing odds to achieve her objective, and just as she's about to get there, she fails through her own folly, or perhaps because she cannot fight fate in the end after all. Ultimately the hero fails; their friend dies; the world ends... our hero dies. Any outcome, as long as it involves the hero's failure in their struggle and the bitter result of it is what makes a Tragedy... a Tragedy.