It consists of two triangular cross-section plates a certain distance apart, with the flat sides 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. In Busemann's biplane, the high pressure shock wave is created internally and reflects symmetrically between the two plates. This cancels/fills the expansion fan forming at the rear, leaving no external shock waves to propagate to infinity. The flat upper and lower surfaces generate no shock waves because the flow is parallel.
The internal alignment of the shock waves means that Busemann's biplane produces minimum wave drag. However, the flat external surfaces and internal symmetry also mean that the airfoil does not produce any lift at the design point zero angle of attack. Hence, no implementation has yet flown, although the concept has been successfully tested in wind tunnels and for ammunition.