Mortgage insurance is a contract that insures the lender against loss caused by a borrower's default on a government mortgage or conventional mortgage. That is, if you don't pay your mortgage, the insurance company "protects" the lender by paying a portion of the mortgage (however, this puts you in default and you'll have a VERY hard time getting credit again).
Mortgage brokers are individuals or companies that work to bring borrowers and lenders together for the purpose of originating a mortgage loan. The broker does not originate or service the mortgages but acts as an agent, often to negotiate with the lender in order to obtain the best possible financing deal for the mortgage borrower.