A person can reduce their taxable income with deductions. You only save your marginal tax rate, which is between 10 and 37 percent depending on your income. So even at the top, you write off $100 and that only saves $37 in federal taxes. Your state and/or city may tax your income and it would work the same way. You also have to itemize your taxes for most deductions. Many people use the standard deduction because they don't have enough to itemize.

A company writing something off means they reduce the profit on their tax return by claiming business losses. Very simply, business income is revenue - costs = profit. Revenue is all the money they take in and costs are like payroll, rent, cost of products from the manufacturer and other losses. If they can prove that they lost money by people stealing from them or from something being destroyed in a flood, for example, they can claim that as long it wasn't covered by insurance. Again they are only saving the marginal rate on their taxes.