The book value of an asset is the value of that asset on the "books" (balance sheet) of the company. The book value is not necessarily the same as the fair market value (the amount the asset could be sold for on the open market).
The book value is calculated as the purchase price of the depreciable asset minus accumulated depreciation on that asset. At some point, the book value may only represent salvage or scrap value, after all the depreciation has been taken. At that point, the asset is considered to be "off the books." That doesn't mean the asset must be scrapped or that the asset doesn't have value to the company. It just means that the asset has no value (or only scrap/salvage value) on the balance sheet.