I understand it to mean what’s called a “deduction”. This is an amount that you are allowed to claim that reduces your taxable income, which reduces the tax you pay. “Writing it off” means claiming the deduction.

Generally speaking, to be a valid deduction, an expense must be necessary and ordinary to running your business. In practice, a valid deduction is whatever your tax authority decides is allowable.

I am answering from the point of view of the Canadian income tax system, but what I describe here is pretty common throughout the world.