Book value is based on an accounting method that only considers certain factors, generally the more tangible or easily quantifiable ones, and excludes the more ethereal factors such as ‘goodwill.’
Book value can apply to an individual asset, a security, or a company, and tends to be pretty straightforward. Whatever value an asset is given on a balance sheet is its book value. For a tangible asset, this is calculated as the cost of the asset minus accumulated depreciation.
For a business, this is total assets minus intangible assets (which includes items such as patents and goodwill), minus liabilities. This is also called the "net asset value" (NAV) of a company, and this is what the shareholders would be able to divide up if the company were liquidated. NAV is also used in the pricing of mutual fund shares.
The book value of a security is the price the investor paid for it, and this is subtracted from the sale price if the investor sells it for the purposes of determining capital gains or losses.