Not everybody does that, it's mostly freelancers or people who own their own companies. For most hired worker - the company they are working for does the taxes and they don't have to save anything.
As for people with their own companies or freelancer - any business got earning but also got expanses, whether is be for materials (like if you have a bakery, and you need to pay for eggs and sugar and all that), Rent - if you have a store or a studio or workshop, salaries for worker, transportation, business lunches and so on. Some or all of those expanses are tax deductible - meaning the amount of of income tax you have to pay doesn't come out from the amount of money that you made, but from the amount of money that you made minus those expanses.
So people save those receipts to prove how much they spend in the last year so that that amount could be deductible from their gross earning.
It's a good thing to save those receipts for 7 years cause sometime the IRS makes inqueries about previous years.