In the US, for qualified charities, you can deduct the full gift from your taxable income, not from your taxes.  So as an example, say you are a "fat cat" making $100,000, and to simplify the example, you have no other taxable deductions.  You pay a 10% tax rate on your first $40,000 of income, and $35% on everything over that amount (simplifying for the example, there are more levels of tax rates).  So your tax bill is 10% of $40,000=$4000 plus 35% of $60,000=$21,000,,,,,a total Federal tax bill of $25,000.  So your income after tax is $75,000.

If you gave $10,000 to a charity such as the American Red Cross, that $10,000 would be deducted from your income for the tax calculation,,,so your income for the calculation is $90,000.  So your tax bill is 10% of $40,000=$4000 plus 35% of $50,000=$17,500,,,,,a total Federal tax bill of $21,500.  So your income after tax is $68,500.

The effect of this is that the charity gets your $10,000 contribution, but since you get a $3500 tax savings, the government effectively pays $3500 of your $10,000 donation--and your after tax income is only lower by $6,500, rather than by lower by the full $10,000.

There are limitations to how much you can deduct each year, but the excess deduction carries over to future years, and I don't think there is a limit on how many years it takes you to use up your deduction.

An important distinction is that the deduction is not against your tax bill in the US, but instead against your tax income--as shown in the example.  I think some other systems do their calculations from your tax payment.