The Wrench is a tool added by Industrial Craft 2. It's used to remove and reorient Industrial Craft's various machines and EU storage devices. To use the Wrench, right-click the machine with the Wrench selected in the hotbar.
Using a Pickaxe on a machine will cause it to drop as a Machine Block, destroying the machine. Using a Wrench, however, is not a guarantee that the machine itself will drop instead; there is a 30% chance that a machine will drop as a Machine Block, even if the Wrench is used.
The Wrench can also be used to reorient the output face of a BatBox, MFE, MFSU or any transformer, which is marked by an orange dot. To reorient the output face, right-click on the face that should become the output face, or hold Shift and right-click to set the output face as being the one on the opposite side. If the Wrench is used on the output face instead, the storage device will drop as an item.
The Wrench is also used to craft its electric equivalent, the Electric Wrench.