Archiving cards gets them out of the way when your team no longer regularly needs them. You will typically want to archive cards when their information is no longer valid. You'll likely also want to archive cards that are created by mistake from time to time.
To archive cards, choose "Archive" from the options menu while viewing the card. Once you archive the card you'll see the archive bar in the footer of the card, which will also allow you to unarchive the card.
We don't have a way to delete cards at present, but it's likely to be added in the future.