The Rings of Alune are part of the ME3 sidequest Silean Nebula: Rings of Alune and can be found on Nevos. This is all the information the official canon provides.
This page is for CDN members' non-canon additions.
The Rings of Alune are named after the asari priestess and artist Alune, who supposedly created the artifact 1500 years ago after a Prothean artifact she never disclosed. They have since been displayed in the Temple of Athame in Astella/Nevos. A Matriarch of the Rings is assigned as caretaker along with an honor guard of Commandos.
The sculpture consist of three individual rings, each warped within itself and all three connected. Important is the coloring which contains biotically illuminated all possible hues of asari skin. The Rings are approximately 50 cm in diameter each and not only defined by their material and shape but also through a biotic charge which keeps them afloat above their pedestal.
The form symbolizes the unitiy of all asari and their colonies. In times of crisis the rings are looked at as a symbol of strength and hope, it encourages every asari to stand in for the other without looking for personal gain.
Small reproductions of the rings are often worn as jewelry or can be found in asari households (also possible in the form of one single twisted ring, symbolizing being a part of asari culture or all three rings connected). Contrary to common believe outside asari space, they are no symbol of bondmateship between individuals, as their legacy specifically encompasses all asari. So wearing or displaying a ring reproduction more likely shows a special affection of an individual asari towards her species.
Rings of Alune reproductions can be purchased in souvenir shops on Nevos and at licensed dealers all over asari space.
It was discussed to move the rings to Thessia about 1000 years ago but a common vote in asari space voiced the strong will that its place on a colonial planet and not on the asari homeworld was an important and integral part of its meaning and it must always stay there.
The only exception to this rule was in 2186 CE when during the Reaper War the Rings where moved to Thessia to inspire the resistance against the Reapers. The rings returned to Nevos after the war.