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If you aren't already logged in, use your preferred email address and password (or Facebook account) to do so. This is the person-shaped icon in the top right corner of your webpage.  This option is at the bottom of the board's icon. It's in the bottom left corner of the board's Edit window. Doing so will permanently remove your selected board from your Pinterest page.
Open the Pinterest website. Click on your profile icon. Find a board you wish to delete. Click on the grey coloured pencil icon on your selected board. Click Delete. Click Delete Board again.