Why is it said that your watch stops when you die?

It's just said meaning that it does not actually stop when you die.

When watches were invented they were very valuable and and a mark of a success. It was extremely dear to the owner. Traditionally a boy received his watch when he turned 18 or whenever he became a man traditionally from a parent figure. He would keep that watch for the rest of his life, and when he died it would be buried with him. Till the 1970's there was a tradition that when a person dies you turn off his watch and bury it in the casket with him. Thus that's where the saying comes from.