What is benefit of tax depreciation?

Strangly - there is no absolutely special aspect to "tax depreciation" than to any other accounting systems form of depreciation - which is a required for concept proper reflection of income and expense.

To simplify the example: When a company buys something generally major -(called a capital asset) it does NOT actually have an expense. It has an asset, say $1,000.000 cash. It simply buys something (say a new piece of equipment). It now is worth the same the $1M is just reflected by the value of the equipment, not the cash.

But under most all accounting systems - that asset is expected to lose value and be used up over a period of time. over that same period's, it is expected to contribute to making money, income. Depreciation just matches the 2 - the economic life of the asset to the cost of getting it.

So (if we presume 10 year life) that 1,000,000 equipment is expense (costs - reduces income) $100,000 a year for 10 years.

For financial purposes -costs are bad, they reduce income. for tax purposes, costs are good, they reduce income!

There may be different determinations about how long something depreciates for, or exactly (arithmetically) it is calculated. Those differences are just a matter of TIMING - as over the time - the same amount - the $1,000,000 is taken as an expense for all systems. Tax generally tries to use the faster methods of depreciation - to get the expense to lower income as soon as possible. (So - speaking it through - say tax managed to expense it 2x as fast as book: 1st five years tax books have an expense greater than tax (lowers income), next five years books has an expense greater than tax (increasing tax income to book by the same amount it decreased the first 5 years. Only a matter of timing).

The advantage to the company - because it has a greater expense for tax sooner, the taxable income is lower, they pay less tax early. Essentially recovering some of the $1,000,000 cash they spent (by paying less tax to the government) earlier than taking longer to recognize the expense.