You have to be either an Account Owner or a Workspace manager to be able to archive Workspaces in your account.
1. How to Archive a Workspace?
You archive a Workspace along with all of its belonging boards. Click the "Workspace Settings" icon of the corresponding Workspace and select "Archive Workspace".
A new box appears with a summary of the Workspace and the Boards you want to archive (Img.1).
If there any unfinished cards on any of the respective boards that box displays their number too. You can click the arrow next to the board name to open the board and check those cards.
Important: If you archive a Workspace, all Boards in that workspace will be archived irrespective of whether you are assigned to them or not.
Once you make sure that you want to archive the board, click the "Archive Workspace" button.
All archived Workspaces in your account are stored in the "Archived Workspaces and Boards" panel of your account and you can access and restore them anytime.
2. How to unarchive a Workspace?
Go to the Dashboard of your account and select the "Show Archived Workspaces and Boards" icon located right to the filter at the left bottom of the Dashboard.
To restore the archived Workspace, you need to unarchive at least one of the boards that belong to it.
You can restore all or any of the archived boards.
The Workspace will become available on your Dashboard.
Note: You can permanently delete a board from the same panel.