There are many activities in this camp, like food fight, roasting diamonds, archery on famous paintings (Mona Lisa, Whistler's Mother and The Scream), playing Quidditch, playing poker about money (and people), telling horror stories that involving financial and business elements like a billionaire told the story about a company's brokerage house being raid by SEC, etc. Billionaires live in cottages with a big dsplay showing how much money they have in the moment.
The Billionaire Camp is a campsite that billionaires like Mr. Burns, Rich Texan, Mark Cuban, Ted Turner, Richard Branson, Jeff Bezos and Mark Zuckerberg attend. It is right next to the Millionaire Camp and is separated by a fence. It is considered extremely dishonorable to be demoted down to that camp as Burns pledged his fellow billionaires to kill him before they threw him out of the fence into the millionaires camp. You are only allowed in this camp if you have over $1,000,000,000 and any billionaire loses their money that reducing their net worth lower than the required amount will be demoted. So far, Burns is the only billionaire of the camp being kicked out after his net worth plunged to $996,036,000 because his stadium was turned into bee sanctuary.
Mr. Burns arrived to this camp with Smithers. He played poker with Rich Texan and won a basketball franchise, the Austin Celtics. When he left, he built a new stadium, but later it is attacked by bees that made their new beehive from it. One year later, Mr. Burns arrived to Billionaire Camp again and told the horror story about these bees, but other billionaires found out that he was four million dollars short of a billion dollars, so he was kicked out, and the billionaires threw him over to the Millionaire Camp for having only $996,036,000. Since it is stated in later episodes that Burns is a billionaire, it is likely he was accepted back into the camp.