Why is the calculation only valid for one year? Do I then have to calculate my footprint again in one year and pay for the compensation?

Yes, because your activities will continue to cause emissions, and these can also vary (sometimes greatly) from year to year. The forest you used to offset your footprint last year is still protected. However, since you are again causing emissions, these should be offset by protecting more forest areas to prevent further CO2 emissions from deforestation and the loss of habitats and biodiversity.

The goal is to reduce your carbon footprint from year to year and to optimize the processes in your company, school or family so that as few emissions as possible are produced.