Our time spent on Earth is finite, and the hourglass reminds us of this. The passage of time never stops, and we're all approaching our own mortal end. Friendly little symbol, isn't he?
There is a duality to the hourglass, though. It can be looked at from the glass half empty v. glass half full standpoint. The first explanation is one that is pessimistic and reminiscent of the glass being half empty outlook on life. Some see the hourglass as being representative of everlasting life because the hourglass can be flipped over again and again. The sand making it's journey from one end of the hourglass to the other repeatedly speaks to the belief that we live on after death. The ivy on the stone, a reminder of the longevity of the soul, supports this optimistic outlook.
For some reason, this stone also makes me think of The Tower card in the Rider-Waite Tarot deck. Anyone else see the similarity?