Humans and chimpanzees are both capable of smiling, and for the same reasons (happiness and fear--see link), which suggests a biological explanation. Both humans and chimps are social animals, and facial expressions are a quick way to communicate one's mood to the rest of the social group. Being able to do so would convey an evolutionary advantage (an individual creating less friction within the community would probably have more mating opportunities and a better chance of passing the smiling trait on to future generations).

As for why we smile (instead of making some other facial expression) for the reasons we do, there is no clear answer. As long as the facial expression is understood by the community as a whole, the exact nature of the expression shouldn't matter. Since a smile is largely involuntary, there must be some connection between the parts of the brain which control emotion and the parts which control the movement of facial muscles, but the nature of this connection remains unknown.

This not a complete answer, but I have heard that people make facial expressions even when they have been blind from birth. This suggests that there is something innate in the origin.