About the feature and how to use it
Closed vs issue closed: Closed is a status type, issue closed is a property of status. By default issues with statuses Closed (and Rejected) will not be shown on the board. It can be changed in board view, Options -> Board columns. If any of your statuses will have the issue closed checked in, issues belonging to this status will have a grey color on the board.
Collapse closed cards option means that you can show only ids, not full cards, for issues belonging to columns (statuses) where you have the issue closed checked in. To set it, go to Administration -> Agile and enable the Hide closed issue data. Remember you have to check in both options issue closed and hide closed issue data for this feature to be working.
This is how it looks on the board:
When you move the mouse cursor on such a card, full info about the ticket will be shown as a hint. Also, cards will be collapsed automatically when moved in closed statuses columns.
Please note these are global settings and will apply to all your projects and boards.