The Federal Housing Administration, commonly known as FHA provides mortgage insurance, backing loans made by FHA approved lenders. FHA backing of these lenders allows them to continue to lend money to qualified borrowers. To be clear FHA does not lend the money, it only insures the banks that do the lending to those that fit into the FHA guidelines. The lenders are at much less risk because the FHA will pay a claim to the lender if a borrower goes into foreclosure on the home and loan. Due to more relaxed guidelines with credit scores and down payment, the FHA allows many people into the marketplace.
FHA is currently the only government agency that is entirely self funded. The FHA costs the taxpayers of the United States exactly nothing, as it is funded entirely by the mortgage insurance that is placed on the loans of borrowers that do not have 20% as a down payment. The most common FHA loan, only requires 3.5% as a down payment.