Gard Otis, a professor of environmental biology at the University of Guelph in Ontario who studies bee behavior, ecology and evolution, explains.
Bees buzz for two reasons. First, the rapid wingbeats of many species create wind vibrations that people hear as buzzes. The larger the bee, the slower the wingbeat and the lower the pitch of the resulting buzz. This is a phenomenon of the wingbeats and not specifically of bees--some flies, beetles, and wasps also have buzzy flight caused by their wingbeats.
In addition some bees, most commonly bumblebees (genus Bombus), are capable of vibrating their wing muscles and thorax (the middle segment of their body) while visiting flowers. These vibrations shake the pollen off the flower's anthers and onto the bee's body. Some of that pollen then gets deposited on the next flower the bee visits, resulting in pollination. The bee grooms the remainder of the pollen onto special pollen-carrying structures (on the hind legs of most bees) and takes it back to the nest to feed to the larvae.
When bumblebees vibrate flowers to release pollen, the corresponding buzz is quite loud. Honeybees (genus Apis) are incapable of buzz-pollination and are usually quiet when foraging on flowers. As an aside, some flowers are adapted to pollination by pollinators capable of "buzz-pollination." Tomatoes, green peppers and blueberries all have tubular anthers with the pollen inside the tube. When the bee vibrates the flower, the pollen falls out of the tubular anther onto the bee. Consequently, bumblebees pollinate these crops much more efficiently than honeybees do.