This is a type of insurance which taken out by you but (and this is crucial) which covers your lender. The MIG premium which you pay is a one-off fee that can cost anywhere between several hundred to several thousand pounds, depending on the loan amount. The MIG protects your lender in the event that you default on your mortgage or remortgage which leads to your home being repossessed. If the lender then sells your property to recover the loan amount owing to them and the sale price of the property isn't enough to cover the debt the lender can then claim against the insurance policy to recover the rest. On top of which, if the claim against the insurer still doesn't cover your lenders debt they will still probably be able to sue you for the outstanding amount under the terms of the mortgage contract.
Most lenders require the MIG fee to cover the proportion of the mortgage or remortgage that is over 75% of the value of the property. What this means is that if you require a mortgage amount of 90% of the value of a property, the MIG fee or premium would cover that 15% difference in the event that you default on the loan.
Which is all well and good but for the fact that if you have decided to protect your remortgage payments by way of another insurance policy (MPPI, for example) you are effectively paying insurance twice over, your own and your lender's. As a result MIG premiums have come under intense criticism in recent years and have in fact been dropped by many mortgage and remortgage lenders.