Stars is one of many organization systems in Gmail.
You might want to star messages for different reasons - to mark it as über-important, as a temporary filing system, or just for fun. If you want to "star" a message, there are several ways that you can. If you are in a mailbox view (i.e. "Inbox," "All Mail," "Sent Mail"), then listed on the very left of the subject line is a small white star - the easiest way to star a message? Simply click on that star, and watch it turn from white to yellow, indicating the change in status from "unstarred" to "starred." One can also use this technique when viewing a message (noting that the subject line will have moved to the top of the page).
If you want to star multiple messages, you can select them using the radio boxes (check boxes) and then select "Add Star" from the drop-down menu at the top of the page.
Unstarring is intuitive once you understand how to star - you can do it by clicking on the yellow star we talked about before, or using the radio boxes (check boxes) and drop down menu.
You can use the operator is:stared in your filters to avoid deleting your starred messages.