Mortgage insurance is like any other insurance there is a person who pays the premiums, that is you, and a beneficiary, which is the lender. This insurance is there for two reasons: one to make sure that the debt is covered if you default and two, to make sure that if something were to happen to you, like death for instance, they would still be able to get their money back. This insurance is the only way that the lender can be sure that no matter what they will get the money that they lent out back from you.
There are different ways in which you can pay your mortgage insurance. Generally the premiums are paid each month along with your mortgage payment but in some cases you will have the option of paying the whole of your premiums at one time, at closing. You will not get to choose the lender that you want to work with for your mortgage insurance in most cases, the lender will do that part for you. All you get to do is pay the payments.