It consists of two triangular cross-section plates a certain distance apart, with flat sides top and bottom parallel to the fluid flow. The spacing between the plates is sufficiently large that the flow does not choke and supersonic flow is maintained between them.
Usually with supersonic flow a positive pressure shock wave is generated at the front and a negative pressure shock wave at the rear. With the biplane, the high pressure shock wave created is only on the inside between the two plates and reflects between the two plates so that it cancels/fills in the expansion fan forming at the rear, leaving no external shock waves to propagate to infinity. The flat sides at top and bottom generate no shock waves as the flow is parallel. The lack of external shock waves means that the Busemann Biplane does not suffer from any wave drag.
Although it has been shown to work in wind tunnel testing, and it has been successfully tested for ammunition, nobody has as yet been able to suggest a practical implementation of the concept for aircraft, as it generates no lift.