DSG stands for 'Direct Shift Gearbox', and prominently features in cars within the Volkswagen Audi Group (VAG), so it's common to see them fitted to cars from manufacturers such as Audi, Volkswagen, Skoda and SEAT.
A DSG gearbox is similar to a traditional automatic. However, it utilises two clutches instead of one, which allows it to shift quickly to the next gear depending on how you're driving.