Volkswagen's Turbo Direct Injection (TDI) is a turbocharged and intercooled diesel engine with "direct injection".
Direct injection engines have the fuel injector mounted in the cylinder wall, instead of behind intake valves. This allows more control over the fuel-air mixure, and when combined with shaped headers, allows for more efficient combustion. This is accomplished by making the fuel-air mixture swirl in high concentrations in a certain portion of the combustion chamber. This results in locally heavy concentrations of fuel, enabling for compression detonation, but the average fuel-air mixture over the combusiton chamber is lower, enabling a more complete burn and higher fuel efficiency.