Book Value per Share is calculate as Total Assets mins Total Liabilities, divided by the number of Shares Outstanding. It is a measure of Shareholder's Equity per Share.
Book Value - or Net Asset Value - per share, is a measure of shareholder's equity and is calculated as Assets less Liabilities and any Preferred Stock, divided by the number of shares outstanding.
From the accounting perspective, it could be seen as the underlying value of a company, whereas the market capitalisation value is dictated by the supply and demand of shares.
However, should the company go into liquidation, the Book Value is often used as a proxy for the value remaining for common shareholders after all creditors are paid.