John Osborne's Ferrari represents everything that sports cars have always represented: the thrill of high speeds, the freedom of open roads, and the overcompensating glory of a mid-life crisis. The only difference in this instance is that said mid-life crisis just so happens to occur during the end of the world.
First, let's establish why the Ferrari is so important to John. The guy is a scientist, which means that he spends his life doing a lot of thinking—but not much doing. Driving a sports car couldn't be more different from his usual routine. But John never thought he'd actually get the opportunity to own one: "It's what I've always wanted to do [...]," he says, but " there's never been any money'" (4.405). In this instance, the apocalypse comes in handy, and John is able to buy his dream car for a pittance.
The experience of driving the Ferrari—of operating on instinct rather than intellect—transforms John Osborne from a mild-mannered scientist into Dale Earnhardt III. In fact, the car becomes so important to him that he chooses to end his life while sitting behind the wheel. That's a big deal. Most of all, it shows that this guy wants to be remembered as John the Racer as much as John the Scientist.