Ryoko is a 700 year old space pirate, and is fond of plundering other worlds with her spaceship Ryo-ohki. She demolished a large part of Jurai, which was the reason for her being hunted down.
It was during a battle with Yosho that Ryoko lost and was imprisoned inside of a cave. It wasn't until hundreds of years later that she was accidentally freed by Tenchi.
Ryoko tries to kill Tenchi and ends up burning his school down and scaring the royal shit out of him in order to show him her eternal gratitude.
In actually, she is only after the jewel in the old sword Tenchi had found in the cave because it was this that gave her her power. Ryoko decided not to kill Tenchi when she realized there was no way that she would be able to beat him. But she never left him alone again.
It became her goal to annoy Tenchi in every way that she could, teasing him incesently and making passes at him. Tenchi isn't aware of it, but she also harboring a huge crush on him. So it's bad new for her when Ayeka comes to Earth from Jurai, and she sees that she now has a rival for Tenchi's attention.
She has two gems embedded in each wrist, and another that she wears as an earring. Because she has these, she is able to create an energy staff and generate blasts. Also, she can use these to summon demons. (one gem is used to summon and the other gem to control the demon)
She can also pass through fly, walls, and turn invisible. (cool, huh?) She has incredible stamina, and I think she is even able to generate lost body parts. (when Yosho cut her hand off, she was able to make a new one) Heck, even her HAIR can be used in her attacks.
Though Ryoko is lazy, irresponsible, brassy, seductive, and couldn't cook her way out of a paper bag, she is always the first to face off with an enemy in order to prevent her friends from getting hurt.