Book value is the price paid for a particular asset. This price never changes so long as you own the asset. On the other hand, market value is the current price at which you can sell an asset.
For example, if you bought a house 10 years ago for $300,000, its book value for your entire period of ownership will remain $300,000. If you can sell the house today for $500,000, this would be the market value.
Book values are useful to help track profits and losses. If you have owned an investment for a long period of time, the difference between book and market values indicates the profit (or loss) incurred.