What do accountants mean by the term depreciation and what is its relashionship to depletionand amortization?

Depreciation is used to expense a fixed asset. When a fixed asset (buildings, equipment, etc... ) is purchased you make an entry to the asset account and an entry to cash or what ever method you used to pay.

In order to recognize the expense, you divide the cost of the asset by the estimated number of years you will use the asset. You then expense this amount every year. This allows you to match the cost of the asset over the useful life of the asset.

For example, you buy a car for $20,000 that is expected to last 10 years. You wouldn't want to consider a car an expense in the first year. You expense $2,000 a year for the 10 year life of the car to evenly distribute the cost of the car.

Depletion is the same concept except for natural resources.
Amortization is the same concept except for intangible assets (patents and goodwill).

There are other ways to calculate depreciation expense and other factors to consider such as salvage value but that is the basic idea behind the concept.