The Net-Book value of an asset is reduced by the same proportion each period. That is, at the end of every period you reduce the value by a fixed percentage. Each period uses the previous period's balance to work out the amount.
For example, we purchase a motor-vehicle for $10,000 and we depreciate it by 10% per month. At the end of the first month we take $10,000 * 10% = $1,000, making the balance $9,000. At the end of the second month, we take the balance from the previous month and apply the 10% factor: $9,000 * 10% = $900. Note the change in depreciation: in the first month the expense was $1,000, but in this month it is $900. At the end of this second month, you subtract the new depreciation amount, resulting in $9,000 - $900 = $8,100. The depreciation for the third month, then, is $8,100 * 10% = $810; the remaining value at the end of the third month is $8,100 - $810 = $7,290. At the end of 12 months the balance would be $3138.11.
The economic reasoning behind the Declining Balance Method of Depreciation is that any asset (think of machinery to stay focused), no matter how carefully serviced by its user, is most productive during the earlier periods of its productive use. Mathematically, the same depreciation rate will extinguish the value of an asset much more quickly under The Straight Line Method than under the Declining Balance Method. In the above example, a $10,000 value with a 10% monthly depreciation rate will be extinguished after 10 months of calculating and recording depreciation by the Straight Line method. But it will take ~22 months to extinguish 9/10 of the value under depreciation using the Declining Balance Method on the same value and with the same depreciation rate. So caution should be exercised when choosing the Declining Balance Method.