In Borderlands 1 artifacts simply added elemental damage to your action skill. In the first released info for Borderlands 2 in GameInformer's December 2011 issue, GameInformer stated that artifacts were a catch-all for any idea that didn't fit into other systems. Paul Hellquist ( Borderlands 2's game design director) said "We have no rules for what it can affect". Possible ideas in the article were percentage chance shots won't cost ammo, increased afterburner length in cars or an aura of healing around the player.
In the newest video of gameplay (the link is on this wikis main page) at 32 min 45 sec is an Eridian object called the Tenacity Relic that gives you 28% additional Second Wind health and is shaped exactly like Rolands artifacts.