As opposed to the common practice of burying loved ones with flowers and placing flowers by the tombstone, Jewish tradition instead puts an emphasis on placing stones on graves.
Jewish authorities likely objected to the flower ritual because of its proximity to pagan customs.
The origin of the stone custom is uncertain, though it may relate to ancient times when a pile of stones was used as a marker. The most common explanation is that placing stones is a symbolic act that indicates someone has come to visit and the deceased has not been forgotten.
A superstitious rationale for stones is that they keep the soul down, based on a belief that souls continue to dwell for a while in the graves in which they are placed.
A more common theme, however, is that stones last for eternity - as opposed to the short life span of flowers. Like the memory our loved ones, stones will never die.