You have to be either an Account Owner or a Workspace manager to be able to archive boards in your account.
How to Archive a Board?
To archive a Board -> go to the main Dashboard, where all your workspaces and boards are located -> click on the Board Settings (the dotted icon) that belongs to every Board -> select Archive Board.
All Archived Workspaces and Boards are stored in the account. They can be accessed and restored anytime.
How to access and unarchive Boards?
To access your archived boards, go to the Dashboard and click the "Show Archived Workspaces and Boards" icon (img.1) located at the bottom of the screen next to the Filter.
This brings up a new panel that stores all archived boards.
The following information for each archived board is available: Workspace name, Board name, Archived by: username and the date a board was archived.
To unarchive a Board, please select the Unarchive icon of the corresponding board and the Board will be restored to your Dashboard.
You also have the option to Delete the Board forever.
Please, read the dedicated article to learn how to archive a workspace.