If you want to hide an item from your view but not delete it entirely, you can archive it. You can archive cards, backlogs, boards and collections.
To archive a collection click the gear button.
To archive a board click the hamburger menu and board options.
To archive an backlog click the hamburger menu and options.
If you have a card in multiple board, backlogs and so forth, and you wish to archive that card everywhere. Open the card and press the Archive button. You will then have the option to archive it everywhere or in just one place.
What's good about archiving is that you can later show these items again. You can do this by either:
Filters in backlogs and boards to show cards
Choosing to show archived items in the collection
Choosing to show archived collections in the collections overview