You can delete any card, backlog, board, collection or user from your organization. You can even delete your organization if need be.
To delete a collection click the gear button.
To delete a board click the hamburger menu and board options.
To delete an backlog click the hamburger menu and options.
If a card lives in multiple places, let's say it has been added from a backlog to a board and then over to two other boards as well. If you're going to delete that card you will have two options. Either you delete the card in one of the places or you delete it everywhere. As shown in the picture below you will have two different options when you press the Delete button on your card.
If you want to hide an item (card, backlog, board or collection) but still have the possibility of restoring it, you can archive it.