The stars next to a Record Match are a “confidence score” for each match. They are based on the degree of similarity of the information in the record (names, dates, facts, relationships, etc.) to the information in your family tree.
This confidence score, a feature unique to MyHeritage, is displayed in the user interface next to each match and ranges from half a star to five stars.
This allows you to filter matches by score and look only at higher probability matches, or extend the scope to look at all matches, likely and unlikely.