I’m seeing a lot of complicated explanations so I’m gonna go with a simpler one.
Say you build a fence for somebody and they pay you $1000. You have to report that income to the IRS. Let’s say the tax rate is 40% so they say “Well you owe us $400.” But instead you provide them with receipts saying you bought $500 of supplies in the form of lumber, screws and such. You have “written off” your expenses and shown the IRS you really only made $500 so you only owe $200 in taxes.