What does it mean to archive a backlog item?

You can archive a backlog item in a Kanban board when you've completed the work on the item. This will move the backlog item to the green archive box at the right side of the board, so that it doesn't take up space in the board itself:

You can unarchive a backlog item anytime you want, for example to resume work on it. Just drag the item back into the board, or use the right-click menu.