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.
In some cases, a pattern is Bind on Pickup, but the crafted item is Bind on Equip. For example, Pattern: Arcanoweave Bracers is Bind on Pickup (whoever picks up the pattern can't sell it to anyone else), but a tailor who knows that pattern can craft the Bind on Equip Arcanoweave Bracers (then sell or give the bracers to someone else).
Some BoE's sell for considerable amounts of gold—such as the epic BoE items that drop from trash mobs in Icecrown Citadel—and are typically rolled on by the raid according to loot rules agreed on beforehand.
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.