having the power of one Gillette

Ok so. The ability to do magic in LOTR is basically the ability to force your will onto the rest of the universe. You want a fire here? Tell the laws of physics to sit down and shut up there's a fire here now. People have different amounts of willpower in this regard based on how close they are in lineage to the Valar, who are the personal first children of the creator deity and helped build the world through song. Gandalf and the other wizards are Maiar, the personal servants of the Valar. The oldest of the elves once lived in Valinor and were created by the Valar as their children, they were close to the light of the Trees and that brought them great force of will. The only elves we ever meet who lived in Valinor are Galadriel and Celeborn.

But elves in general, descended as they are from these origins, have a deeper and closer relationship to the Valar than other species. Humans and dwarves never lived in Valinor. (Not all the elves did either, it was a whole thing, but the Mirkwood elves had never been to Valinor and so were less powerful than the others. This is why Legolas is a relatively low-power elf, though still more powerful than most humans.)

There was, however, a nation of humans, the Numenoreans, who lived on an island halfway between Middle Earth and Valinor. Because of this, they had as much power as humans are capable of. After Numenor sank into the sea, they founded Gondor, and that is why the line of kings of Gondor is so powerful. They are directly descended from the original Numenoreans. Each generation after that first, however, had slightly less of that power, and because human lifespans are short (and grew shorter as they decreased in power), there are many more generations of humans between Numenor and the third age than there are of elves. Though the elves have seen a diminishing of this as well, it's much slighter. This is why Elrond has much less power than Galadriel.

Many many generations of humans ago, but only a couple generations of elves, the elven princess Luthien fell in love with a human, Beren. Because Beren was part of the line of Gondorian kings, this gave a sort of power boost to their children and thus to the line of kings after them. This is why Aragorn is so much more powerful than other humans: he's a direct descendant of an elven princess.

Alright so. Magical objects. Magical objects come in two sorts: those made of a substance with special properties or inscribed with words of power (the Lothlorien cloaks, the Earendil glass that Frodo has, the Mithril coat) and those made by the creator placing some of their own will into the object (the palantir are one example. The Silmarils are another, although Fëanor also captured the light of the trees in them which added to their power).

All the Rings are the second type. Celebrimbor was the one who developed the method for making them. He was the grandson of Fëanor and so had a fuckton of power and will to use for that.

Sauron was a Maiar, like Gandalf and the other wizards. He had been Morgoth's second in command and apprentice, but after Morgoth fell (he was a Valar btw), Sauron claimed to be reformed and became an apprentice of Celebrimbor. He learned the secret of creating the Rings, and had a hand in shaping the Seven and Nine, and he put small pieces of himself into them. The Three elven rings were made after Celebrimbor realized that Sauron was up to shady shit, and so he never had anything to do with them.

Then Sauron made the One Ring, and he poured a TON of himself into it.

But the way these kinds of objects work, anyone can use them if they have sufficient willpower to channel what's already in the object. But there's a catch. Because the source of the object is literally someone else's willpower, the object is always primarily subject to the creator's will. It's literally a part of them, will act in ways that person would want, and responds to commands from them even if someone else is trying to use it.

This is why the people keeping the elven rings (Gandalf, Galadriel, and Cirdan) have to be so powerful themselves. Even though these rings aren't evil, they have a limited level of desire for certain things and would actually eventually take over the mind of someone less powerful. Also they were trying to keep Sauron from finding them. (Aside, this is why the One Ring has no effect on Tom Bombadil. Whatever he is, he natively has more will than what Sauron put into the ring.)

So. If you have the One Ring, whoever you are, you can channel a level of Sauron's will commensurate to your own. Gollum never could use it for anything but turning invisible. Frodo could do hardly anything deliberate with it. But if Gandalf or Galadriel had it, they could fuck shit up. If Aragorn had it he would be terrifying. Even Faramir could have gotten a big power boost from it. And because it's part of Sauron, who craved dominion over others, it wants you to use it to dominate others, and it will tell you that you can, and that it will help you shape the world into something you want.

But here's the catch: it's a fucking liar, just like Sauron. Sure you'll be powerful if you have it, but it's got his will in it, and the more you do what it wants, the more control it gets over your mind. In fact, it's so powerful in that way that just being around it can get to you. That's what happened to Boromir. That's why Gandalf, Galadriel, and Aragorn know they absolutely cannot touch it or even try to keep it safe. They know, or fear, that they would eventually give in and try to use it for good, but it would corrupt them too. Faramir knows what it is, and he rejects the whole idea of having that much power. Sam recognizes it for a liar, and rejects the power it offers him.

(Sauron was also massively weakened when he lost it because once you put that much of yourself into something, you can't get it back out.)

Tolkien, who lived through both world wars, saw a lot of what happens when people are given too much power and influence over others. He was also a devout Catholic, and there's a lot there and in the wider mythos about the dangers of seeking power because at some point you're setting yourself up as a false god, but the prime false god in the Catholic mythos is Satan. And Satan will offer worldly power to people in order to gain control of them.