Here's a little history for you, I don't know much behind them but here's what I do know. These gems that Ryoko has contain Washu's goddess powers. Over 20,000 years ago, Washu possessed equal power to that of her two sisters, Tsunami and Tokimi. This is why the power in Ryoko's gems is the same as that of Jurian trees which derive their power from Washu's sister, Tsunami.
The whole reason that Washu created Ryoko in the first place was so that she could harness the powers within her gems. With all three gems in place Ryoko can use the power that Washu once held, including 10 Lighthawk wings. During Ryoko's creation, Washu's assistants Kagato and Yakage each exploited Washu's creation of Ryoko. Yakage stole some cells and made a clone. Kagato just imprisoned Washu and brainwashed Ryoko.
For centuries the galaxy's most brilliant scientists have researched the gems but they reveal little about their origin or how they work. The closest replication of the gems was achieved by Kagato. He managed to create gems more powerful than Ryoko's but they were not nearly as compact. They were so large that he had them mounted on his ship the Soja (which Washu created.) When Ryoko was under the control of Kagato she had all three at once. But after her battle with Yosho, she was stripped of all three.
Ryoko can create lesser versions of the gems. They each take about 750 years to create and are very fragile. Ryoko wears an earring on her right ear; this is one of her created gems. One major drawback is that Kagato used the gems to control Ryoko and that's why he was able to control her. Although she did possess all three gems when she fought Yosho on earth, she was fighting Kagato's control with all her power which is how Yosho was able to take the gems from her.
One gem, left wrist: Summon Minor Demons, Control Minor Demons, Summon Major Demons
One gem, Right wrist: Control Major Demons
Three gems, neck: With all three gems in place, Ryoko is able to fulfill the purpose that she was created for. Ryoko is able to tap into the gems which actually contain Washu's goddess powers. They were sealed away long ago for unknown reasons. Ryoko can create 10 Lighthawk wings just like Tsunami can.