An item is Bind on Equip (BoE) if it becomes soulbound when equipped by a player character. A warning appears before a player equips a Bind on Equip item for the first time, asking if the player is sure they want to do so.
In other words, it may not be traded or placed on the Auction House after being equipped.
The term BoE is also used for designs or patterns that may create a BoP item. Example: "The Robe of the Archmage is BoP, but its pattern is BoE".
Note that the in-game tooltip actually displays the words "Binds when equipped", that's why some conservative players use "BwE", but "BoE" appears to be more popular.