When you click "Open Items" your event is now live, and attendees are free to bid on silent auction items, purchase raffle tickets, and purchase your fixed price items.
"Publishing" an item makes it visible to your attendees, whether or not your items are open. Unpublishing an item hides it from your attendees.
Why unpublish an item? Say a local restaurant has promised to donate a $100 gift card to your auction, but hasn't delivered it, yet. You can still create an item card, but keep it unpublished so attendees don't think you're auctioning an item that you really don't have. When the restaurant delivers the certificate, publish the item, and you're all set.
Unpublished items display this icon on the bottom of the item card.
To publish and unpublish items, from the "Items" tab on your manager site, click to open the item, and toggle the switch at the bottom.