Orders queue from the pre-market and are matched in one print at 09:30 New York time. The exchange publishes an indicative price and imbalance for several minutes beforehand, which is why the last few minutes before the bell often show a strong directional pull toward the projected open.
The opening print is the official open on charts and the reference for many intraday strategies, including the opening-range. A direct-listing uses a specially supervised version of this auction to set its first trade.
Example: the auction shows a 1.8M share buy imbalance against a $46 indicative. Sellers step in during the final minute, the imbalance shrinks to 300,000 shares, and the open prints $45.10 rather than the $47 the imbalance implied.
Related: closing-auction, reopening-auction, pre-market-session, opening-range, direct-listing