Artifacts are special items gained by playing online with other people. Once received, you can rename them if the icon on the item has a feather pen next to it. Once renamed, the artifact gains new abilities (Can only be equipped by Cosmos characters, etc;) and will be able to be equipped. Once renamed, an artifact can never be renamed again.
Players can only have 20 artifacts at a time. Unwanted artifacts can be sold, normally for a very high price.
The type of Artifact you receive depends on what your online opponent has equipped. For example, If Zidane fights Firion, who is wearing a 'Bronze Bangle', Zidane may receive an unequipable artifact named 'Nameless' with identical stats to the Bronze Bangle. Once Zidane renames 'Nameless', it can be equipped.
Artifacts can go from player to player (Though a player never loses his/her artifact; their opponent will merely get a copy), gaining in strength as the item grows in owners. If Zidane's 'Nameless' (Now renamed to 'Air Brace') goes to Terra after an online match, Terra will receive a stronger copy of the 'Air Brace'. Zidane might even get the same artifact again when fighting Terra again, except it will be stronger. Artifacts can therefore become extremely powerful if they go through multiple owners. Eventually, Zidane may have an item much of a much higher quality than his original Air Brace!
On a side note, Artifacts cannot be accessories, nor can they be obtained by fighting ghosts.
Helpful Tip: If you get a Nameless artifact, save your game BEFORE you rename it. That way if you get a new ability you don't like, you can reload your game and rename that artifact again for a diffrent ability.