Bind on Account, or BoA designates an item that "binds" to the account of the character who first picks it up. These types of items could be passed between different characters on the same account (presumably by using the shared stash), but could not be traded to another other characters.

There was to be no item binding of any kind when Diablo III launched, but it began to enter the game with the Legendary ring rewarded by the Infernal Machine special event.

Early Bind on Account Stance

While the developers mentioned the possibility of BoE or BoA on items in Diablo III, they ultimately decided against any form of item binding in the game.

Prior to that decision, BoE was expected, while BoA was considered unlikely. The theory behind item binding is that when top level items can be traded, the economy gets glutted and eventually every character has the best of everything, since characters who indulge in huge amounts of item finding (or illegal duping, in the case of Diablo 2) will score enough of that item to distribute them widely.

Compare BoA to BoE -- Bind on Equip which is also known as "soul binding." These types of items bind to the character who first equips them; they can be traded, perhaps only within the same account, but once any character actually uses the item, it is bound to that character permanently. (Characters can dispose of such items for space considerations, but they can not give or trade them to other characters.)

Blizzard Comments

Jay Wilson addressed this issue in an interview from BlizzCon 2009. [1]

Jay Wilson: We have no “Soulbound” or bind-on-pickup, except for quest items. We do have bind-on-equip for the highest end items in the game. We targeted, roughly, any item above level 85. These we will do as bind-on-equip. The reason for this is that we want people to be able to trade them, but we also want to remove the high-end items from the economy. One of the greatest ways that you can do that is with bind-on-equip. What we don't want is to have a situation where you find something on the ground like, “Oh, man. This would be a perfect weapon for my Monk. Oh, but I just picked it up and now it's on the wrong character.” We don't want that at all.

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.

Bashiok addressed this issue during a mini-interview posted as part of Blizzcast #13, in February 2010. [2]

Zarhym: Will all Bind on Equip or Bind on Pickup items be bound to account? So you can hand them down to your other characters as you find better gear.

Bashiok: 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. [3]

Totally, which is why I said “But there could be economic reasons that we don’t do that.”

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.

Anyway, we’re not really seriously considering BoA items at this point in time.

Binding was finally ruled out in April 2011, by Jay Wilson in an interview with Diablo3.cc. [4]

I’m happy to announce that we recently decided there will be no binding of items in Diablo III. They will be freely traded for the life of the item. The only way we are going to do any kind of binding would be for things that are not progression-sensitive. Like we might say…a quest item. We don’t want you to be able to give to other player to short circuit a quest, but if you find a sword, piece of armor, or gem....anything that you find in the ground, once you pick it up, you can freely trade it... forever.

References

August 2009: Game Director Interview by G4TV.com.
February 2010: Bashiok on Blizzcast #13.
February 2010: Bashiok forum post.