Terra Branford is the half esper heroine of Final Fantasy VI aka Final Fantasy 3.
As is common in these "struggles against the Evil Empire stories, as the story opens, Terra is something of a Buffalo Soldier, fighting for the empire that has enslaved her, albeit under the control of a mind control helmet. However, after the military mission she goes on finds its target, a long lost esper, her psyche gets a shock, and she begins to realize who she is.
Thus begins the long, convoluted tale of resistance and heroism that Final Fantasy VI is. There is no "main character" in this game, although Terra is one of the larger players. As the game progresses, we learn more about her, including the fact that her mother was human and her father was the esper Maduin. About one quarter into the game, Terra turns into an Esper, and goes somewhat insane. Later, however, she learns to control her transformations. In the game play, she can turn into an esper upon command, and deal some serious damage.
After the world has its change of life and becomes a barren, apocalyptic wasteland (umm, this isn't a spolier since this pretty much has to happen in any anime type story), Terra settles down to take care of a bunch of small children in a wasted, burnt out town somewhere on the East Side of the game map. However, after some soul searching, she rejoins your party and goes back to dealing some serious damage.
At the very climax of the game, when the party gets together to fight Kefka and give their speeches, Terra claims to have found out "what love is". I may have been too busy playing the game to pay attention, but I am not actually sure who exactly Terra fell in love with. But in any case, she triumphantly learns both how to beat people down, what love is, and how to deal with her heritage. All in all, a pretty uplifiting message.