Depreciation is the annual deduction for the cost of an asset that is used up over time in a business or income-producing activity. Internal Revenue Code section 167(a) allows "a reasonable allowance for the exhaustion, wear and tear (including a reasonable allowance for obsolescence)" of property used in a trade or business or held for the production of income. Section 168 then supplies the actual system most taxpayers use, the modified accelerated cost recovery system, which assigns each kind of property a recovery period, a method and a convention.
The word is worth separating from its everyday meaning, because the two senses come apart in a way that costs people money. In ordinary speech, depreciation is a thing losing value: a new car worth less the moment it leaves the lot, or an insurer paying the depreciated value of a ten-year-old roof. Neither of those is a tax deduction. Tax depreciation does not track what an asset is worth at all. It runs on a statutory schedule applied to what the asset cost, and it exists only where the asset is used to earn income.