A wrench is a tool - the English call it a spanner - that is usually operated by hand, and is made for tightening or loosening bolts, nuts or anything that needs to turn. Solymon Merrick patented the first wrench in 1835.
The physics of a wrench are that the tool works as lever. There are notches at the mouth for gripping. The wrench is pulled at a right angle to the axes of the lever-action and the bolt or nut. Some wrenches have mouths that can be tightened to better fit various objects that need turning.