The tradition of placing stones on graves comes from the Jewish religion and has been used for centuries. Although the origins are not quite clear, there are a few stories that try to explain it. This custom can be seen at the end of the movie "Shindler's List" where the survivors and their families visit Shindler's grave and place stones on it.
Flowers versus Pebbles
Putting flowers on graves to remember a loved one is a custom embraced by many religions. Placing pebbles on the grave is a Jewish tradition. While flowers wither and die, stones last forever. It is a reminder of the family's presence, and it lets people know that someone visited the grave who cared about the deceased.
In ancient times, headstones were mounds of stones. Visitors would add a pebble to the pile of stones to show respect for the dead. Some believe that the tradition of leaving pebbles on a grave is simply a carry over from the time when headstones were just piles of stones.
Some believe placing pebbles on graves started as superstition. It was believed the souls of the departed would rise out of their grave and haunt those left behind, but the placement of pebbles or stones on the grave was thought to prevent them from rising up.