A driver’s logbook is used to document the distances traveled with a vehicle and the reason for each trip so that the shares of personal and business use of the vehicle can be determined. It can then be used for the submission of details to the tax office or within the company of employment. The following information is recorded in the logbook: driver, place and date of departure, mileage at the beginning and end of the trip (distance traveled), and purpose of the trip.
Source: Wikipedia, edited (only available in German)