How Do Minimum Delivery Interval Days Work?

By default, it has zero (0) days. It means you can process same-day delivery.
If you add (x) minimum delivery interval days then it will simply disable the (x) number of days in the delivery calendar starting from the current date.
For example, it is the 3rd of March today and you have set 2 delivery days then it will show the available delivery days from the 5th of March in the order delivery date calendar.