Reputation is very important to keep as high as possible as it directly impacts how much cargo your vessels will have on board when the departure on their routes.
Various factors impact the reputation such as yourCo2 balance, how well you do your fleet maintenance, the quality of the vessels in yout fleet, the age of the vessels in your fleet. On top there is a small random factor.
You can boost your reputation by doing marketing campaigns. The reward can be very high by running marketing campaigns, but plan your marketing with consideration, as the reward only comes if you are online to depart your vessels.