Hi @mirko.bruhn, this is a rich discussion which I think can be helpful for you in understanding how rewards help in selecting the next state.
Rewards is linked with what next state of lander should be, Like if lander is in a state where moving left earns more reward than moving right, then to maximize the reward the lander will move toward left. Reward is linked with current state but it is calculated by taking account for other states (In case of lander it is Reward at Left End or Right End and steps to reach there).