[pg 76, Unweaving, The Path of Daggers] These barbarous rustics offered too many surprises. A way to Heal being severed, however imperfectly. That was impossible! Except that they had done it. Involuntary rings. Those Warders and the bond they shared with their Aes Sedai. He had known of that for a long, long time, but whenever he thought he had the measure of them, these primitives revealed some new skill, did something that no one in his own Age had dreamed of. Something the pinnacle of civilisation had not known! - Moridin
Many people are confused about what "Involuntary Rings" are. Clearly they are something that was not discovered or used in the Age of Legends.
Evidence
[Glossary of A Crown of Swords: Linking]
...Entering a link is normally a voluntary act, requiring at least acquiescence, but under certain circumstances, a sufficient circle already formed can bring another woman forcibly into the circle as long as no man is part of it. Insofar as it is known, a man cannot be forced into a circle, no matter how large...
[pg 122, The Breaking Storm, The Path of Daggers]
The Tower studied this [forming circles, involuntarily] for many years long before the Trolloc Wars... It was the problem of men who can channel that drew them to it... Men can be brought into a circle, too, and as the circle doesn't break even if you go to sleep. . . . Well, you can see the advantages. That was an utter failure unfortunately. - Sareitha
Summary
This basically explains it. A 'Ring' is another word for a circle or a link. Sareitha says that the Tower studied this. Why did they think it might be possible for men to be brought into a circle? Clearly the Tower had discovered that it was possible for a woman to be forced into a circle, so they did some experimenting with forcing men into circles. Why was it an "utter failure"? Because the Tower could not find a way to force men into the circles. This is fairly clearly the "Involuntary Rings" referred to by Moridin.