In one line: An offer with no financing contingency, closing on the buyer's own funds.
A cash offer needs no lender, so it carries no financing or appraisal contingency and can close in a week or two instead of thirty to forty-five days. Sellers value the certainty and often accept a lower price for it; on distressed homes and at trustee sales, cash is the only form of payment accepted.
Cash still uses escrow and title, still allows an inspection contingency, and still pays closing costs, just fewer of them. Proof of funds, a recent bank statement or a letter from the institution, takes the pre-approval letter's place with the offer.
The rent vs buy calculator gives the cash a buyer does not spend credit for what it would have earned; a cash purchase forgoes that return, which is the real cost of the certainty.
A worked example
Two offers on a $400,000 listing: $405,000 financed with a 40-day close and an appraisal contingency, or $392,000 cash closing in ten days. Many sellers take the cash; the $13,000 is the price of certainty.
Questions people ask
Do cash buyers still get an inspection?
Yes, if the contract keeps the inspection contingency. Cash removes the financing and appraisal contingencies, not the inspection. Only at a trustee sale is there no inspection at all.
What is proof of funds?
A recent bank or brokerage statement, or a letter from the institution, showing the cash to close. It takes the pre-approval letter's place with a cash offer.