The FHA is not a lender nor does it build homes.
The FHA exists to insure lenders against loss in the event that a homeowner defaults on a mortgage.
Mortgages backed by FHA are often called "FHA loans" even though it's somewhat of a misnomer. A more appropriate name would be "FHA-insured" loans because that better describes the FHA's function.
With the FHA's guarantee, mortgage lenders are enticed to make loans on which they would otherwise pass and the explicit backing from the government holds mortgage rates low for borrowers.
FHA loans are often used by borrowers with less-than-20-percent downpayments and, therefore, tend to require mortgage insurance payments.
For FHA loans above 80%, mortgage insurance rates are 0.50% annually (paid monthly) with an up-front payment of 1.5% against the loan size and due at closing.
Homeowners with 15-year fixed FHA loans, however, are exempt from the annual insurance payments.
For all homeowners, though, when the loan balance reaches 78 percent of the home's value, the annual MI is no longer required.
Mortgage rates for FHA loans are typically higher than comparable conforming mortgages but because of new, risk-based pricing from Fannie Mae and Freddie Mac, homeowners with credit scores under 680 are finding FHA a viable alternative.
And often with lower rates.
Source
FHA Loan
Wikipedia, April 1, 2008
http://en.wikipedia.org/wiki/FHA_loan