A two-shaft turbocharger is designed to be a solution that allows an engine to produce boost across a wide range of airflow, while being more compact than a sequential turbo set-up. It also allows for high boost levels like larger turbos, but doesn't sacrifice the bottom end torque as much.
What's the secret to a two-shaft turbo? It uses two different styles of compressors. First, an axial compressor forces air into a radial compressor, which then increases boost further. Using variable vanes for both the intake and the exhaust turbines, the turbocharger can provide useful boost across a wide rev-range. It's like the combination of a jet turbine, an automotive style turbocharger, and a variable geometry turbocharger all in one. Sound complicated? Check out the video for full details!