@John S. Mortgage payments are paid at the end of a month so to speak. If you close on June 1 your first payment is due July 1. If you close on June 2 I believe your first payment would be due Aug 1. You skip the July 1 payment. I guess if you are selling a house as well you could skip your June payment if you sell in June and roll it into the payoff then close on your new property and not have a payment due until Aug 1 so would have skipped June and July payments.
@Rob Beland That's a fallacy. You can only skip one months payment, irrespective of when you close. Your payments are either rolled into the old loan's payoff amount, or you end up prepaying the partial month at closing.
I am currently in the process of refinancing my primary residence. We are skipping two payments. We are closing on July 8th , and we will be skipping the July and August payments. However, I am sure that @Upen Patel is correct in that the skipped payments are rolled back in to the old loan which will obviously increase the amount of your new loan.