You can mark any issue in Jira as your personal favorite, just open issue and click star icon:
You can use the star dropdown to add the issue to a separate favorites list:
The main goal is to use the star as a field that can be added to the issue for searching:
Another convenient way to utilize the star is to view filtered information in the gadgets:Also, you can use star on the issue search screen, just add star column to the list:
Finally, you can manage your favorites in Jira gadgets: