This is one of those things that I'll bet research will eventually verify: "baby led weaning". Here's an article that introduces the topic. The idea became publicized when a child care expert for UNICEF said that it was unnatural for babies to be on pureed foods for long periods of time. Instead, babies should be introduced to solid foods directly at six months. (Disclaimer: this is not medical advice!)
This research suggests that when a baby can pick up something and lift it to his or her mouth, that a baby is capable of chewing. This also makes evolutionary sense. Babies that could pick up food and chew would obviously be better off than babies who could only pick up food. Hunter-gatherer parents often helped with this process, by giving pre-chewed food to infants. However, this type of weaning was probably much different than the long period of pureed foods used with modern infants.
More information on this approach is available here.