For example, Iron Pipes have one output port and many input ports. In order to change which port is the output, you need a Wrench. The output is indicated by the port that does not have a little gray rectangle on it.
Wrenches are also very helpful when you discover that you placed something the wrong way. They will rotate every Engine, so if you have two Quarries separated by a 1-block space, you can put an Engine in that space and it will power one of them. However, the best design would be to not put anything in that space and place your Engines on the other side of the Quarry blocks.
This current page refers to the BuildCraft Wrench.
See Wrench (Forestry) for the Forestry Wrench. Note: the Industrial Craft wrench is compatible with all Forestry equipment, but not the other way around. Unknown compatability issues aside, this tool is effectively obsolete.