All weapons and armors in the game can be enhanced once you get access to a blacksmith, although some merchants will be able to do it as well. Every piece of equipment that can be upgraded starts out at 0 stars and in order to upgrade it, you need to have certain items, as well as gold. Each piece can be upgraded up to three stars, after which, there are special enhancement levels.
DRAGONFORGING
Dragonforged is a special enhancement level that is only obtained by having an item equipped on the Arisen when one of the dragonkin is killed. This includes the Drake, Wyrm, Wyvern, The Dragon, and the Ur-Dragon (which is divided into the offline and online versions). Equipment on pawns cannot be Dragonforged, as well as equipment in your inventory. Note that only equipment at the time of the dragon's death counts, so you could switch equipment right before its death.
Only killing the The Dragon and the online Ur-Dragon allows a piece of equipment to be Dragonforged 100%, without having to enhance it at all. All other dragons have a chance to upgrade your equipment to Dragonforged, although the equipment must be upgraded to at least one star. At 3 stars, the Drake, Wyrm and Wyvern have a 18% chance to Dragonforge equipment, while the offline Ur-Dragon has a 30% chance.
RARIFYING
Dark Arisen grants the opportunity to upgrade equipment to a level above Dragonforged. There are two extra levels, dubbed Silver Rarefied and Gold Rarefied, which will require specific items and Rift Crystals instead of gold. Note that equipment must be Dragonforged before you can upgrade to Rarefied levels. Barroch on Bitterblack Isle is the only NPC who can Rarify equipment.