From Final Fantasy
IV, she's at first a young caller (revised as "summoner
" in later translations) girl whom you meet in a village after you and your friend accidentally destroy it in a fire along with her dragon mother in the cave that you went through to get there. Rydia totally hates you for doing that, but eventually learns to forgive you. She then joins your party and becomes a pretty okay spellcaster.
Later on, she gets swallowed by Leviathan
and is sent to the Land of Monsters. The flow of time is accelerated there, allowing her to rapidly grow and quickly become an adult. However, she also loses all of her powers as a white mage
, but at the same time learns a bunch of awesome black magic spells and summons.
From then on she returns to your party and becomes one of the most kickass
characters in Final Fantasy history, along with being a combination black mage/summoner and having really nice-looking green hair
. You can't beat that, folks.
Rydia is a strong character who is able to overcome her fears and doesn't let anyone push her around. You just don't have cool characters like the ones in Final Fantasy IV anymore, sadly.