While Mandarin's rings each grant a different ability, including mind control, illusion creation, and time manipulation. Together, the rings make Mandarin a godlike being, and in one of his most ambitious plans ever, the villain attempted to force Iron Man to make them the centerpieces of his deadliest armor ever.
Recently, Marvel Comics introduced a new set of Ten Rings wielded by Shang-Chi which more closely match how the movies re-imagined them. However, the original Ten Rings have long belonged to the Mandarin, who salvaged them from a Makluan spaceship in his youth. The Mandarin later claimed that they weren't rings at all, but rather futuristic storage devices each used to hold the memories and abilities of an ancient alien warrior. These warriors wanted new bodies capable of leaving Earth, and there was no-one better to create them than the armored Avenger.
Unfortunately - as depicted in Matt Fraction and Salvador Larroca's Iron Man arc 'The Future' - the Mandarin was able to hack technological advances Iron Man had made to his body in order to force him to create the Titanomechs. These incredibly dangerous suits were an idea Tony had developed but resolved never to actually create. Sadly, through a combination of trickery and control, the Mandarin put him to work. The Titanomechs were wildly powerful suits already, but once piloted by the alien consciousnesses inside the Ten Rings, they also gained the abilities of their assigned warrior. Thankfully - due to a desire to retain control of his empire and the army of tech-based supervillains he'd enslaved to help Iron Man - the Mandarin didn't commit all the rings at once, giving Tony the slight edge he needed to destroy the towering suits before they destabilized Earths' core in an effort to return to the stars.
Thankfully, Iron Man was able to win out against the three Titanomechs he was forced to build, but only with some serious back-up. It took Iron Man, a cadre of villains willing to turn on Mandarin, and the superteams known as the Triumph Division and the Dynasty to keep the Titanomechs at bay, and they were only beaten due to an experimental swarm of trillions of nanobots Tony's company had set loose to find where he was being held. In short, it took Iron Man's allies, enemies, and most experimental tech to even the playing field, and he'd still probably have lost if the Mandarin had been willing to give up more of his rings to the project.
While Iron Man's armor and Shang-Chi's Ten Rings pack a punch in the movies, their combination in the Titanomechs turned the merged technology into a world-class threat. Worse, it underlined how dangerous Tony Stark is even when he's responsible. Iron Man is capable of deg world-ending weapons that no-one else could even fathom. In a world of telepaths and manipulators, his knowledge is dangerous by itself, and in the past he's even deleted designs from his own mind to stop them ever being realized.
Tony Stark's blessing and curse is that whenever he conceives of a problem - from everyday annoyances to apocalyptic chaos - he also conceives of the suit of armor that can fix it, but each suit comes with its own consequences. In the case of the Titanomechs, even conceiving of these powerful suits gave the Mandarin's rings a reason to enslave him and end the world. Shang-Chi's Ten Rings and Iron Man's armor turned out to combine into the ultimate weapon, but Tony is always learning, and that means that as deadly as the Titanomech armor proved to be, he's already started thinking up something worse.
