Colloquially, the term “tax write off” has been used to mean one of two things: 1) a tax deduction for expenses against taxable income, or 2) a tax deduction due to a partial or total loss, also against taxable income. In both cases, it’s a deduction from the amount of income which the tax rates would apply toward. To be clear, neither would be a tax credit, which is a form of direct reduction in the tax amount to be paid.
The first category includes business expenses, such as amortization of the cost of office furniture, usually over a number of years. This can also include expenses which the government deems especially worthy, such as mortgage interest expenses in the USA.
The second category is for calamities, economical or natural disaster related. Someone losing their coastal home due to land erosion could write off their home, because that asset is now worthless. Or an investor can write off their shares in a film production, if the main actor turns out to have done awful things and no one wants to work on the film anymore. In this category, an asset has been involuntarily or voluntarily given up, with no hope of a recovery, and so the tax code usually allows this to be a deduction against income.
To be clear, a taxpayer cannot just randomly designate stuff to write off. The first category is wholly defined by policymakers, and the second category requires an irrevocable declaration of the asset’s worthlessness, such that a future (unlikely) recovery will be a new, separate taxable event.