The star indicates that a moped is available at a special promotional rate.
When you select a moped marked with a star, a green shaded area will appear on the map. If you end your trip within this green area, you will receive a discount on the cost of your ride.
In concrete terms:
If the total duration of your trip is less than or equal to the number of minutes offered, your trip is completely free.
If your trip takes longer, you only pay the difference between the actual duration and the free minutes offered.