Proof of funds is a document, usually a bank or brokerage statement, that shows a buyer has the money to close a cash purchase. A seller can ask for it before signing a contract, since an offer with nothing behind it is only a promise. A buyer with real money to close should be able to provide it without being pushed.
Why it matters
Asking for proof of funds is how you find out whether a cash offer is real before you take your house off the market.