Terra's half esper and as has been stated before her morphed mode is her letting her esper side loose. This isn't spoiler for the sealed gate because Rahmuh tells you this when you're at WoB Zozo (Both times).
As far as how morph works battlewise, all I know is second hand information. What I've heard is that it doubles her Magic Power and Attack Power for most of her attacks. Most but not all barrier piercing, nonelemental attacks are excluded from the morphed boost (Ultima, Flare ect.). When you morph, the bar that appears repusents how much time that you have left while morphed. The more time you have, the slower it will go down. If you change back, you'll be able to save your remaining time. The battle timer increases when you gather Magic Points after a battle and eventually will max out at either 128 Magic Points or 255 (I forgot which).
As I've said, it's all second hand knowlege but it does come from some reliable scorces. Neat art by the way. *Saves a couple of pieces.*
