A conforming loan is a mortgage that is less than a specified value. Currently (November 2001), the threshold is $275,000 (for a single-family home in the continental USA, always 50% higher in Hawaii and Alaska). Mortgages that do not "conform" is a jumbo loan. Conforming loans are much easier to qualify for, and also offer lower interest rates.
Basically, conforming loans arises due to the secondary mortgage market. When you get a mortgage from a bank, they usually turn around and sell the mortgage to someone else. The bank makes money immediately, and the buyer is willing to pay now to get the long-term pay-off. This is good, because this frees up capital so that the bank can finance more home purchases.
The major buyer of these mortgages are FNMA, or "Fannie Mae", and FHLMC, or "Freddie Mac". These federally-mandated corporations were developed to help people to buy houses. But these organizations don't buy mortgages above a certain threshold, as there is higher risk involved with bigger loans. So conforming loans, which the banks can sell easily, offer better terms than jumbo loans.