Beeswax is the most natural of all waxes. It is produced by one of three types of honey bees, the worker bee (the other two types are the drone and the queen). Worker bees have specialized glands that make wax which, when they eat honey, is secreted from their bodies in small clear flakes. They then chew the flakes and build honeycomb.
Other natural waxes, like soy and palm, have to be extracted from plants and processed in order to be used. While they too are natural waxes, beeswax still has the advantage of being harvested and used in its all natural state (though, yes, cleaned/filtered). Paraffin is, of course, a petroleum byproduct extracted through chemical processing.
An additional advantage of beeswax is that, when burned, it produces negative ions, which help remove pollutants from the air. Beeswax candles also burn slower, giving a longer burn time than other waxes.