Negi's magic ring is a magic amplifier that allows him to use magic without the use of his staff.
In volume eleven, as Negi is practicing in Evangeline's resort , Evangeline gives him a ring which, when worn, allows Negi to cast spells without the aid of a wand/staff, so that during the Mahora Festival Tournament, Negi doesn't have to worry about carrying or losing his staff in battle.
After the festival, when Class 3-A ambushed him in the baths, he lost in the confusion. Akira helped him look for it and Yuna eventually revealed that it had fallen into her bath kit. Yuna, Haruna, Misora, the Narutaki Twins and Zazie played 'keep away' for a short time before Akira reclaimed it for him and return to Negi.
He also made use of it to conjure up a sleep-inducing fog to fool Ako into thinking that a disastrous encounter was just a bad dream. He had no choice but to use it for a time, after he had lost his staff during the disastrous encounter with Fate in the Magic World.
Negi's ring is presumably designed originally for an adult or teen at least, as it is so big the ten-year-old has to wear it on the index finger. It has a steel plate screwed to its body with an engraving stating "Virga annulata quae movet artem magicam" (The staff-ring which activates the art of magic). According to the engraving, this makes the ring essentially a miniature staff/wand in ring form, which allows to use it as casting focus. Unlike the staff, the ring is worn on Negi's primary casting hand (his right).