PMI or MI also known as private mortgage insurance, is an insurance required on all FHA mortgage loans (regardless of down payment amount) and Conventional loans (whenever the borrower(s) come in with less than 20% down payment). Mortgage insurance was created to help insure the lender so that in the case of default, the lender gets paid by the mortgage insurance provider.
There is an option for lender paid mortgage insurance or borrower paid mortgage insurance with Conventional loans. What this means is that either the borrower(s) can pay the mortgage insurance on a monthly basis(borrower paid) or it absorbed within the rate as is the case with lender paid mortgage insurance. Generally speaking, lender paid mortgage insurance carries a higher rate due to the mortgage insurance being included within the rate. In many cases however, the total mortgage payment comes up lower with the lender paid mortgage insurance option on Conventional loans. There are also options to pre-pay a portion of the mortgage insurance, to reduce the monthly premium.
In short, the goal is to refinance to remove mortgage insurance as soon as the 20% equity requirement is met.