In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
In the case of a bow and arrow, when the archer does work on the bow, drawing the string back, some of the chemical energy of the archer's body is transformed into elastic potential energy in the bent limb of the bow. When the string is released, the force between the string and the arrow does work on the arrow. The potential energy in the bow limbs is transformed into the kinetic energy of the arrow as it takes flight.