The option applies a filter on the macro status "closed" (idle), that appears on the "treatment" part as a checkbox.
It is not directly related to the Status, even though the default configuration is set so that closed status checks the "closed" checkbox.
But playiong with configuration you can have the possibility to have an item that is in "closed" status, but checkbox "closed" is not checked.

Thanks a lot for your reply. but I d'ont really understand the usefulness to have the closed status and checkbox not always synced ?

In my case, I do a very simple test :
1/ I create a ticket and I closed it (in the "ticket page") => the closed ckeckbox is checked and the ticket is really closed (OK for me)
2/ I create a ticket, I drag and drop the ticket in each column (in the kanban page) until the Closed column => the closed ckeckbox is unchecked and the ticket is not really closed.

There are several impacts :
  ==> the ticket is displayed in the tickets page with closed option not checked
  ==> I can modify information on a closed ticket (strange)
  ==> I can't close my activities linked to the ticket because Projeqtor says that they are linked to an open ticket...

I understand that the "closed" option is linked to the "closed checkbox" in the ticcket and not the status. Now I know how to correctly close my tickets (with this checkbox).
But is it normal that, when I use the kanban Board to close a ticket, this closed checkbox is not checked ?

Thanks a lot

But is it normal that, when I use the kanban Board to close a ticket, this closed checkbox is not checked ?

It may bez linked to an issue we fixed on V9.5.3.
Which version are you using ?

Thanks for your reply.
I actually work on the v9.2.2 on production and v9.5.3 on pre-production. The issue is still there on the 2 versions.

Thanks a lot