I saw earlier wrist watches do not need any cell to work. They are required to move the key attached on side of watch and it works for 24 hour and then we need to again move it. Explain its working.

A mechanical wrist watch works by winding a spring. When you move the key, the spring inside the watch (it is called mainspring) starts winding. This stores the potential energy in it. The potential energy of the spring is used to run a gear system inside the watch which moves the respective hands of the watch.