A ring was an item of jewelry worn on a person's finger.
In the alternate reality of 2259, Khan Noonien Singh sent an explosive device in the form of a Starfleet Academy ring to Thomas Harewood. After Harewood received the ring, he dropped it in a glass of water, which caused a massive explosion that destroyed the Kelvin Memorial Archive in London, England. (Star Trek Into Darkness)
Doctor Leonard McCoy could be seen wearing a ring throughout his time in Starfleet. He wore the ring on his left hand pinky finger. (Star Trek: The Original Series; Star Trek II: The Wrath of Khan; Star Trek V: The Final Frontier)
According to Mess officer Breil, rings were among the objects seeming to disappear on the USS Enterprise while the ship was orbiting the planet Cepheus in 2269. (TAS: "The Terratin Incident")
Q wore a silver ring while dressed up as a French marshal in 2364. (TNG: "Hide And Q")
Lwaxana Troi was the keeper of the "Holy Rings of Betazed", an artifact. In addition, she wore rings matching her outfits. (TNG: "Haven")
Anne Jameson wore a wedding ring while visiting the USS Enterprise-D in 2364. (TNG: "Too Short A Season")
The holographic Minosian peddler wore several rings on both hands. (TNG: "The Arsenal of Freedom")
Curzon Dax wore a ring on his ring finger, which left a scar on Benjamin Sisko's face. When Jadzia Dax tried it on, it slipped off. (DS9: "Dax")
In 2369, Quark tried bribing Odo with a suit made of Andorian silk and a ring made out of pure sorax, without success. (DS9: "Q-Less")
The Kazon-Nistrim used a poisoned ring with a needle to kill people. (VOY: "State of Flux")
Augris' species wore a single ring in the bone-structure on their nose bridge. (VOY: "Resistance")
Osyraa wore a ring that allowed her to remotely control the transporter on her flagship, the Viridian. (DIS: "The Sanctuary")