Instead of bending thin sheets of wood veneer into a circle and gluing multiple layers to form a shell, stave drums start out as solid pieces of wood that aren't bent and are therefore unstressed wood. This also allows for a very wide variety of woods to be used in drum construction and far less glue than ply drums. Ply drums come from long cylinders cut into shorter drum shells. Stave drums are made for each particular drum and aren't a long tube chopped up into a number of different drums.

Ply Drum Construction-Overhead view

Stave Drums Use Less Glue

Stave drums start out a number of solid pieces of dried wood.  Typically twice as many staves as lugs on the drum.

Overhead View:

After being glued up, the drum looks like this.

The squared off edges are lathed off on a metal lathe.

Shells can be as thin as 1/4" up to as thick as you want.