They're basically so you can ride your horse in a halter a little bit easier, since you can just clip the reins to those rings on the nose instead of tying the reins on or whatever people do.
Personally, I'm not a huge fan of those. I have one that I made were the rings are halfway between the nose knots and the chin knot which I like pretty well. I feel like having the rings on the nose knots like that encourages the nose to slip around and be less reliable. It doesn't slip if the rings are farther down, it's just more work to make one with the rings farther down.
Fabio - 13 year old Arabian/Lipizzan gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.