A book build is a method of determining the optimal price at which to offer securities to the financial markets.
The first time a company offers its securities for sale (in an Initial Public Offering), there is a danger of undervaluing the securities. There are 2 main types of securities issued by companies - ordinary shares and debt instruments. In the case of shares, undervaluation means the price asked is too low, leading the company to sell too many shares. In the case of debt, undervaluation could lead to the company offering to pay too high an interest rate. In either case, the company loses money. A book build prevents this by asking market players (usually large securities trading firms aka institutional investors) what price they are willing to pay for those securities. The offers received are compiled in an order book (hence the name, book building) and either a weighted average or the highest price received is taken as the offer price upon which allotment is done. The actual process of computing the price to offer is called price discovery.
The alternative to a book build is a fixed price offer, which has the failings discussed in the preceding paragraph. Another danger of fixed price method is overvaluation, where the offer fails because investors think the offer price is too high. When this happens, the underwriters have to buy all the outstanding securities, usually at a discount to the offer price. This reduces the profits earned by the investment banks (investment banks generally don't lose money regardless of the situation).
Brevity Quest 2021