The Federal Housing Administration (FHA) is a government agency that was created in 1934. This agency provides mortgage insurance to lenders who meet its standards and requirements. In the context of the law, mortgage lenders who are not FHA-approved typically will not be able to qualify for this mortgage insurance from this federal government entity.
If mortgages are defaulted on, it can have severe consequences for the lenders who gave them. The reason is because mortgages are typically worth a lot of money: hundreds of thousands of dollars. So, by providing a government agency to offer mortgage insurance, the government tries to create stability and security in the mortgage market. The goal is for this security to give confidence to lenders to keep offering mortgages so that more people can qualify for them and buy houses.