BillboardGUIs are Global User Interfaces that can be adornees to bricks in the actual physical ROBLOXian world, unlike the ScreenGUI. While the BillboardGUIs do not actually display GUI objects, they can have objects like TextButtons inserted in them as if they were a ScreenGUI, except these buttons will be usable and visible while their according part is in the player's vision rather than all the time. The downside to this is that because the GUI is a 2D object, the GUI's contents will always be facing you, making for an ugly look.
Edit June 21, 2013; ROBLOX has messed up BillboardGuis which have a Background Transparency of 1. The text in the billboard flickers and a box covers the text. This also effects bricks with the name 'Head' in a model which have a humanoid value that makes the brick have text over it equal to the model name.