The underwriters function as the broker of these shares and find buyers among their clients. A price for the shares is determined by agreement between the company and the buyers. When shares begin trading in a public market, the lead underwriter is responsible for helping to ensure that the shares trade at or above the offering price.
When a public offering trades below its offering price, the offering is said to have "broke issue" or "broke syndicate bid". This creates the perception of an unstable or undesirable offering, which can lead to further selling and hesitant buying of the shares. To manage this possible situation, the underwriter initially oversells ("shorts") to their clients the offering by an additional 15% of the offering size. In this example the underwriter would sell 1.15 million shares of stock to its clients. When the offering is priced and those 1.15 million shares are "effective" (become eligible for public trading), the underwriter is able to support and stabilize the offering price bid (which is also known as the "syndicate bid") by buying back the extra 15% of shares (150,000 shares in this example) in the market at or below the offer price. They can do this without the market risk of being "long" this extra 15% of shares in their own account, as they are simply "covering" (closing out) their short