There's a word for the trope she represents, although I don't know how widespread the name is outside of TVtropes. She's a broken angel. We learn that she was destined for greatness, about to enter Celestia's School for Gifted Unicorns, the same dream Twilight herself had.
But the Ursa Minor changed that, of course. Imagine Rainbow Dash suddenly losing the ability to fly, or Fluttershy losing the ability to communicate with animals. Or Rarity losing the ability to express herself artistically. That's what sets the stage for Tempest, that incredible loss of what was meant to define her.
But she doesn't mope about, or grow depressed, not for long anyways, she's determined as all hell, so she goes out into the world, crossing continents searching for a way to get her dream back. You can understand why she walks a slippery slope towards evil, and see how, had circumstances been different, even some of the mane6 might have done similar things.
Tempest is probably the most well-written tragic villain in the show. Not necessarily how her dialog and arc in the movie itself is written, there are a few hickups here and there (although I'd say she still ranks quite highly, but I haven't done a side-by-side analysis.), but in how her meta-story is set up and how her themes are handles, how closely she mirrors other prominent ponies.