When you defeat Sif, the Great Grey Wolf you will be granted the Covenant of Artorias. The ring is removed from your inventory at the start of each play through.
Once the Four Kings have been defeated and the Bonfire lit, you can remove the ring. If you do not wear the Covenant of Artorias when entering the The Abyss for the first time, you will simply die.
If you are summoned to help defeat the Four Kings while playing online, you will also need to wear this ring - even if you have defeated the Kings in your game.
Sif, the Great Grey Wolf. The guardian of the grave of Sir Artorias, the Abysswalker.