The price of a security at the beginning of a day of trading on the stock market.
When a stock exchange opens, each security has an initial trading price at which it is bought (and sold) on the first trade of the day. Quite often, the security's open price will differ from its closing price of the day before. This is because the trading price at the close of market on the previous day is no longer an accurate indicator of a stock's value - news may have come out since that impacts the company; there has been trading on foreign exchanges while the domestic exchange was closed; and there has been a flow of buy and sell orders overnight, since the previous close.
A stock's closing price from the previous day serves as a benchmark indicator of the stock's performance that day. If a stock finished at a lower price than where it ended the previous day, it is said to have "closed down;" likewise, if its price is higher at close than at the previous day's close, it is said to have "closed up." Price changes in the stock are also commonly expressed in relation to a stock's previous day closing price, so when looking at the percentage change in a stock price on a chart, in the newspaper, or on a website, this number is relative to that stock's closing price of the previous period (day, week, month, etc).
The calculation of open price differs depending on the stock exchange. On the New York Stock Exchange, for example, open price is calculated by a specialist that looks at his or her book of orders. The specialist then selects the price that will execute the most buy and sell orders that were place after hours, and create the most liquidity in the company's shares.
On the NASDAQ, open price is calculated differently through an Opening Cross system. Market makers on the exchange post a single bid and ask price. After all market makers have seen the first round of bids and asks, they revise their prices and trade executions happen at a single initial price that is intended to accurately reflect supply and demand.