What is a Tanzania Peaberry?

A very popular Tanzanian coffee is the peaberry type, and there are a couple of theories about why that's so. Peaberries seem to have a mystique about them. What's a peaberry? It's when a single bean develops inside the coffee cherry, instead of the familiar two "flat beans." Why so many fans of the peaberry? The theory is that all the goodness of the coffee cherry is in only one bean, rather than split among two.