That is insurance paid to insure the lender against default when the loan amount is more than 80% of the value of the property, or purchase price, whichever is less.
Private Mortgage Insurance is privided by various companies, Genworth, Radian, PMI, to name a few. The rates vary based on credit score, loan to value, property type, etc.
MIP, or Mortgage Insurance Premium, is the insurance provided by FHA.
There is an up-front fee for MIP, but not PMI. The monthly premium on MIP went up so much recently that PMI is now starting to look like a much better deal, especially for those with good credit scores who don't have much to put down. Another great feature that can be done with PMI, that is rarely used, is what is called the Super Single Premium by some companies, not sure what others may call it. This is a 1 time fee paid at closing so that no monthly PMI amount is paid. The borrower can either pay it up-front, have a credit back from the lender to cover it by paying a higher rate, or a combination. I was once asked by a client why everyone doesn't do this, and I told him it was because most loan officers don't know enough about it to either advise about it at all, or know how to present the option to borrowers.