If a borrower does not have enough money to pay for the required down payment, it is permissible to have a relative give the borrower the money for the down payment.
With an FHA loan, the entire down payment amount can come from a relative. The gift donor must sign a letter stating that the funds do not have to be paid back. The donor must be able to show that they are able to provide the funds (a bank statement showing the money has not just recently been deposited into their account is sufficient), and the borrower must show receipt of the funds (a bank statement or deposit ticket is needed).
With a conventional loan, the rules are slightly different. A relative can give a gift to the borrower for the down payment, but the borrower must contribute the minimum required down payment themselves (usually 5%). The exception to this is if the gift is for at least 20% of the purchase price. Then, the relative can give the borrower the entire down payment and the borrower doesn't have to contribute any money at all. The documentation requirements are slightly different, too. The donor does not have to show that they are able to afford the gift - they just need to show that they have given it to the borrower. The borrower still needs to show that they have received the gift, and the gift letter still needs to be signed.