You will sometimes have important messages that you want to easily access for the future. By using the star feature, they will be moved to your starred folder and indicated with a colored in star.
Click the star to the left of the senders name to move the message to your starred folder.
Or select multiple messages and click on the 3 dots and choose "Mark as Starred"
Even if you archive a message or move it to another folder, it will still appear in your starred folder until you un-click the star.