It means that in essence you would sign a promissory note for the balance of what the surgury cost is and make direct payments to him.
Say the total cost of the surgery is 15,000 and his portion of that(his fee) is 6000. Then the rest of it is supplies, OR fees, anesthesia cost, etc.
If you can come up with 12,500 (7500 loan & 5000 cash) that pays for everything except part of his fee. It is not unheard of in this scenario for the surgeon to go ahead and do the surgery and accept payments over the next 6-12 months for the balance. This is not common practice but it has been done many times.
Generally you will need to be able to cover all costs and at least 1/2 of his fee for him to consider it.