From Diablo Wiki
Binding ("Soul Binding" in WoW) refers to items that are locked to a character or account once they are found, picked up, or equipped (depending on the particular rules for that item in a particular game). Binding is most often incorporated into a game to limit trading, either by removing items from the economy (once they are equipped they can not be traded) or to force players to find their own gear (bind on pick-up or account items can't be traded at all).
Some fans who felt unsatisfied with the Auction House economy in Diablo 3 tried to play the game self-found (AKA Ironborn) for a greater challenge and sense of accomplishment. Ultimately the Diablo 3 developers came to agree with them, that it was more fun to find gear than to buy it, and changed almost everything in D3v2.
Binding History in Diablo 3
There was no item binding when Diablo III launched, but subsequent patches added binding for special materials and crafted items, and then for practically everything in Diablo 3 version 2.
- Patch 1.0.5 added the Infernal Machine, and made all materials (keys and organs) used to create Hellfire Rings as Bind of Account, so they can not be traded or sold to other players.
- Patch 1.0.7 added five new level 63 crafting recipes, and the gloves, shoulders, bracers, chests, and amulets created by these recipes are all Bind on Account.
- D3v2 and Reaper of Souls use binding for almost everything. All legendary items, crafting plans, gold, materials, gems, and many other items and commodities are Bind of Account.
- The small exception is that legendary (or Set) items can be traded (given) to other players in the game when the item was found, for up to 2 hours after that game ends.
Item Binding Basics
The basic types of binding. Diablo 3 uses BoA in almost every instance.
- Bind on Account "BoA" -- Items can be shifted between characters on the same account, but not anyone else.
- All Hellfire Ring materials, the crafted bracers, gloves, chests, shoulders, and amulets added in Patch 1.07.
- Bind on Equip "BoE" -- Item can be traded freely, but once equipped can only be used by that character.
- No BoE items exist in Diablo 3 as of September 2013 in Patch 1.08.
- Bind on Pick-Up "BoP" -- Items that are locked to whichever character first picks them up.
- During early development most quest items were BoP and stored in a special inventory tab so players couldn't lose or drop them and prevent quest completion. By launch all such items had been removed or made virtual, mostly by tweaks to the structure of the quests.
Binding Coming in Reaper of Souls
After various high quality BoA items were added in crafting recipes in Patch v1.07, the developers liked how they worked in the game economy and there are plans for many more binding items in the Reaper of Souls expansion.
This concept blew up over time and eventually virtually everything, item or material or gold, became Bound to Account in Diablo 3 version 2.
Item Binding During Diablo 3's Development
Most of our focus on Diablo 3 is as a trading game. So, if you take trading out of the item space, you ruin the core of the game. Finding a really great item that is not for you is still a great event because it means you have a bartering tool to get the item that you do want. We definitely want to make sure that that still exists.
Maybe. It sounds kind of cool. So I asked Jay and some of the other designers about this actually because I wasn’t sure, but Jay’s response was “That sounds awesome!” And he likes things that are awesome. Which is a very Jay Wilson quote. But there could be economic reasons that we don’t do that, there could be gameplay reasons we don’t do that. It’s probably too early to say, but that sounds cool so we’ll have to see.
Bashiok elaborated on this later that same day, when a fan pointed out that BoA could lead to stagnation in the economy, if every account eventually had several of the best items that players could pass around between their different characters. 
Anyway, we’re not really seriously considering BoA items at this point in time.
It would probably stagnate the economy… UNLESS, there are other systems in place that could make it attractive for players to essentially destroy their BoAs. So I don’t think it’s without solution at least, but it could get sticky if not balanced or pulled off just right.
Binding was finally ruled out in April 2011, by Jay Wilson in an interview with Diablo3.cc. 
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