What does the green gun do in AntiChamber?
The green gun serves two purposes:
It can place lines of cubes via a thin beam - you can use it to place cubes in otherwise blocked off areas (thin "slots" on walls). It's as simple as pressing and holding the left mouse button.
It can be used to quickly delete existing cubes - like the blue gun, only faster. While on the surface it may seem like just being able to do what you already could do faster isn't much of an improvement there are a few moments where this comes in handy.
In a line of cubes, deleting a cube NOT on either end will cause the smaller section to vanish. If done in the middle, then all the cubes will vanish. (Also, it's what murgatroid99 wrote, to give credit where credit's due!)
Placing cubes in a closed loop (a minimum of 8 cubes forming a 3x3 square empty in the middle), will cause it to be filled in the middle. This can be used to create more cubes when you're missing some.
The green gun can create lines (possibly bending) of blocks by holding the left mouse button. These lines can act as fuses: when you divide a line of blocks into two lines by removing a block, the shorter line (or possibly both) will start disappearing from the point of the removed block. You can use this to remove a block far away at a time delay.