The purpose of depreciation is to match the cost of a productive asset (that has a useful life of more than a year) to the revenues earned from using the asset. Since it is hard to see a direct link to revenues, the asset's cost is usually allocated to (assigned to, spread over) the years in which the asset is used. Depreciation systematically allocates or moves the asset's cost from the balance sheet to expense on the income statement over the asset's useful life. In other words, depreciation is an allocation process in order to achieve the matching principle; it is not a technique for determining the fair market value of the asset.
The accounting entry for depreciation is a debit to Depreciation Expense and a credit to Accumulated Depreciation (a contra-asset account that is reported in the same section of the balance sheet as the asset that is being depreciated).