The ring of feather falling is a common magical ring found in many fantasy role-playing games.
This particular ring is most often a brass band (no silly, not a brass band that plays music), with an engraved feather pattern (or alternately, pictures of birds).
The feather fall ring keeps the wearer from being damaged in any fall. The ring detects acceleration, and works to slow it down to a halt. After falling just a few feet, the wearer will slow down to about a foot per second (plenty slow enough to cause no damage from even the highest mountain). One interesting side effect of the ring is that it works sideways as well (not just up or down). A character tossed by a giant, or shot out of a cannon would move at that same ludicrously slow pace. An athletic character can use this to their advantage to jump very long distances, like Morpheous in The Matrix (this works as long as they drop a few feet over the course of the jump)..
This ring is the only fantasy equivalent to the parachute (which had not been invented yet). Most of them are in the hands of people who ride flying steeds of various types (which allows them to survive an unexpected fall).
This is only my interpretation of this item, which is based largely upon its use in the older versions of the Dungeons & Dragons series of games. Your ring of Feather Falling may be totally different, so always be sure and read the instructions.