We use this setting to include closed case statuses in the Case Status field. This lets user to quickly close the cases without using the Case close button.
Setup > Customize > Case > Support Settings
Currently on case detial page we have status field with New, Escalated and Working picklist values.
Support Settings > Edit (Enable: Show Closed Statuses in Case Status Field)
When “Show Closed Statues in Case Status Field” was enabled in “Support Settings” now we can see “Closed” value in the Status field.