Part art, part social experiment, but mostly an attempt to spread goodwill. A "smile rock" is a small rock or stone with a smile drawn on it. The smile rocks are left in public places (where no one will trip on them or otherwise be injured by their presence) in the hopes that whoever needs to find one will do just that.

By reminding people to smile. A small smile can do wonders to a person's attitude, improving their day and changing the way they interact with others, creating a domino effect of kindness and goodwill.

Two reasons. First, rocks are unobtrusive. Putting one on an empty table outside a restaurant won't harm anything.
Second, contrast. Smiles are powerful, but fleeting, the existence of an individual smile is temporary and short-lived. A rock, on the other hand, is seen as strong, unchanging, powerful, and more-or-less permanent. A rock acts as a strong foundation on which to spread smiles.