This article explains what it means when there is a green star next to an offer.
What does it mean if there is a green star next to an offer?
A green star next to an offer means that the offer is unconditional. An unconditional offer means no contingencies or conditions are attached to the offer that would prevent the sale from occurring (e.g. offer is pending inspection or appraisal, offer is financed).
For example, if a buyer submits an all-cash offer and removes all contingencies, the offer would be considered unconditional.
Unconditional Offers are shown on the Offers tab and the Timeline tab under the Property Details page, as shown below.