Guess jewels are fancy stuff to put your power in, huh? Better buy insurances against burglary and volcano fire though.
Originally, rings of power were made by Elves to preserve their power. Sauron guided them in the making of those 'magic rings', and so learnt of ways to bind their power into his own rings. Sauron also made rings for the Dwarves and Men, to bring them under his power too. He kept a residental part of his power in the Ring so as to make the binding more potent. Note: "One Ring to rule them all, One ring to find them, One ring to bring them all and in the darkness bind them."
The power of the Ring extends Sauron's might to such that he bring all other races under his fold without making war. Of course, this never came to be, since the Dwarves could not be enslaved with jewellery (you need chains and cat-o-nine-tails), and the Elves never used their rings openly. Also, everyone hated him for cheating them and struck first before he could gain complete control. But if Sauron were to have the Ring again after his long holiday in Dol Guldur, he could probably achieve what he could not have done one age ago.