If you select to close on the first of the month, you would have the ability to capture all of that month's interest in the next schedule payment due the first of the following month. Otherwise the first payment would be two months out and the borrower would owe a full month of interest at closing.
The closing of the loan being on the first of the month, allows the Lender to adjust for this scenario - first scheduled monthly payment as a whole month of interest. On the GoDocs docs, Inception Date is the date of first full month of interest that will accrue to set the rest of the dates.
Checking the box allows the Lender to control the inception date of the loan docs, which is an option that exists when the Lender happens to close/disburse on the first of the month. It allows you to consider if you want to collect a short month interest or not.