The term book value of equity refers to the net worth of a business. It consists of the total assets of the business minus the total liabilities. For publicly-owned corporations, you will find the book value of equity listed on balance sheets in annual reports, usually as "Shareholder's Equity."
For accounting purposes, the book value of equity is divided into several components. These include the par value (original asking price) of common shares and of preferred shares. In addition you may see categories like "capital in excess of par" if the stock originally sold for more than par value. The most important category is often retained earnings. Retained earnings are the total of all earnings during the company's lifetime that have been reinvested rather than being distributed to shareholders as dividends.
For investors an important measure is the book value of equity per share (BVPS). To calculate BVPS, divide the total book value of equity by the number of outstanding shares. For example, if a company has total book value of equity of $25 million and 5 million shares outstanding, you have $25 million/5 million shares = $5 BVPS.
Book vs. Market
Book value of equity is a very different thing from the value of the company's shares on the stock market. The price, or market value, of a stock depends on what investors are willing to pay for it. Companies whose performance is good may have share prices greater than the book value. A company that is faring badly will see its stock trading for less than the BVPS.
Naturally enough, most investors are mainly concerned with the market price of shares (that is, how much they can buy or sell the shares for). The book value of equity is important as a measure of whether or not a company's stock is a good buy at a given price. When the market price is above the book value of equity, it indicates the market thinks the company is undervalued or that it's earning prospects are good. By the same logic, when a company's stock is priced less than the book value of equity per share, the market is saying either the company's earnings are poor or its assets are overvalued on the company balance sheet.