The Federal Housing Administration (FHA) is a government agency that helps people who wouldn't be able to get a mortgage loan otherwise. They do this by offering insurance against the principle balance of the loan. The FHA knows that owning a home is a good and powerful thing, and it also knows that many people don't have perfect credit but could still make a mortgage payment. Because of this, the FHA will work on behalf of the borrower and offer insurance to calm the worried lender. This insurance says that the policy will pay back the lender if the borrower doesn't pay back the loan.
When lenders see this kind of insurance coverage, they are more likely to give loans to people who would not get loans based on standard criteria and requirements. Since the government is backing the loan, the lender has very little to lose. Only the interest (profit) is at risk of being lost. Mortgage lenders who work with FHA loans have slightly different requirements for approval, but a borrower could still be turned down for funding. Just because you have FHA insurance does not mean that anyone can get a loan.
In the same way, the FHA has its own rules about the types of loans it will insure and the total amount of money it will cover. When a borrower is in this situation, the types of loans they can get are often limited to those that FHA has already approved, and the lenders must meet FHA's requirements to be on the list of organisations with which FHA will work.
There is no complete list of all the loan types or lenders who work with FHA loans, so a borrower or mortgage broker may have to do more research to find these lenders. In either case, a borrower needs to know exactly what it means to have an FHA-insured mortgage and what other requirements need to be met before they can get approval.