You own it. That's the whole difference. In a standard assignment you sign a contract to buy from the seller and then sell that contract to someone else for a fee, and the deed goes straight from the seller to the end buyer. Your name never appears on it. In a double close, the deed goes from the seller to you, and then a second deed goes from you to the end buyer. Two closings, two deeds, and in between you're the legal owner of a house.
That gap is usually an hour or two on the same day, sometimes a couple of days. The tree comment isn't a joke. Risk of loss generally passes to the owner, and if something happens while you hold title you're the one dealing with it. In practice people manage this by keeping the gap as short as possible and by asking the title company to close both legs in one sitting.
The part that isn't obvious from the outside: because you're a real owner rather than someone selling a contract, some states treat the whole thing as an ordinary purchase and resale instead of unlicensed brokerage. How that applies to you depends on your state's statute, so an attorney where you operate is the person to ask.
You also need money for the first closing. Either short term transactional funding, or a structure where the end buyer's funds cover both. Neither one is free.