Like most rich people his wealth is purely theoretical. If I needed to demonstrate my entire wealth I could just extract it all from my bank account, but a lot of his money is based on perceived worth of his businesses, which of course don't really have a value because they haven't been sold to anyone and in many cases haven't actually generated a profit.
So basically the IPO is saying that if the company was sold, it would be worth x amount of money. But of course we don't know that, and unless he actually sells the business, he doesn't get x amount of money.
This is what people mean when they say we are in another tech bubble, companies are getting massively overvalued for what it is even remotely conceivable somebody would be prepared / able to pay for them. So you get stupid headlines like this that say that Elon Musk is a trillionaire, even though he has substantially less than 1 trillion dollars in his various bank accounts. In terms of actual dollar amounts he probably has 10 or 20 million at most. Absolutely not chicken feed by any stretch of the imagination but also not more money than most countries GDP.