This is the date from which interest on your mortgage is calculated. For example if your transaction closes on the 27th of the month, but you would like payments to be on the first of the month, your IAD would be the 1st of the next month.
If your IAD and your closing date are not the same date you will be required to pay the interest on your mortgage for the period between your closing date and the IAD. In the example where you took possession on the 27th, assuming a 30 day month, you would be responsible for 3 days of interest on the mortgage amount. Some lenders will deduct this from the original mortgage advance meaning that you will have to make up that shortfall at your lawyers. Some lenders will just deduct this amount directly from your bank account.