Why do Jewish people put stones on peoples grave stones?

Based on a verse in Samuel, we pray of the deceased that "their soul should be bound up in the bundle of life." The Hebrew word which we translate here "in the bundle" (biTsror) also means "a stone." And it is grammatically related to the name of God used in Deuteronomy ch.32, "Tsur", The Rock. The Torah uses that description for God to signify His steadfastness. So the placing of a stone for the dead shows our hope and prayer that he/she should be steadfastly bound with God.