To elaborate a bit on /u/Fritschya's answer...

Even the official NASCAR brags about its links to moonshining/bootlegging. To quote Jack Smith:

It was rough and rowdy. It was lots of boys just out of the service - they had been there four or five years in them wars - and I would say that at least 70% of the men that was driving the cars in '46, '47, '48 and on up was involved, or had been involved, in what we called trippin' whiskey, haulin' whiskey, maybe makin' a little bit of whiskey. And not only the people that was racing, but the people that owned the race tracks. They was just as bad as the race drivers. They had made lots of money during the war sellin' whiskey and different things, and then they come in and built a nice track where other people didn't have the money. Some of the best race tracks that there is today was built with that kind of money.

Now there are two types of bootlegging. During the prohibition bootlegging was simply about getting alcohol to the customers. This alcohol either took the form of locally produced moonshine or more or less legitimate forms of alcohol smuggled across the Mexican border or brought in by ship from the Gulf of Mexico. These imports by sea made bootlegging especially prevalent in the South. Following the end of prohibition in 1933 bootlegging continued, although on a much smaller scale, transporting illegally produced moonshine. Bootlegging essentially became a form of tax evasion. Demand for tax-free locally produced liquor remained high.

There are two aspects of bootlegging that played directly into stock car racing's popularity in the South. First, there's the most simple and direct link: bootlegging allowed racers to hone their talent and acted almost as a selection process, as in the long run the best racers were the least likely to get caught. It also encouraged mechanical knowledge - how to get the most speed out of ordinary consumer cars. Bootlegging was as much an informal training ground for mechanics as it was for racers. On top of that, once you had the cars, it didn't take much to throw an impromptu race together. Even if the purses of these races were relatively small they were often a source of local bragging rights.

There was however also a cultural aspect to the bootleggers. To many in the South they were almost like modern day Robin Hoods, standing up against the tyrannical Federal government and its prohibition laws. Many of the most successful bootleggers became local legends for their ability to repeatedly thumb their noses at the law. This resonated in particular with people in the South, where the idea of the federal government as tyrannical was pretty much part of the identity ever since the Civil War. Those who could successfully push back against that federal government and defy its oppressive laws were seen as heroes.

That's not to say that the relationship between bootleggers and NASCAR promoters was always perfect. Prior to World War II stock car racing was already popular, although highly disorganized, with a poor reputation due to many unscrupulous promoters who would scam both the racers and local organizers. Following World War II NASCAR was founded in order to legitimize stock car racing. Bill France Sr., the founder of NASCAR, had moved to Daytona Beach, Florida during the depression. Daytona had always been a popular destination for motor sports enthusiasts. France never liked the illegitimate background of the bootleggers but in order to make NASCAR a success he needed their technical expertise, financial backing and local celebrity status.

Unfortunately the number of purely academical sources on the history of stock car racing is very limited, a lot of it would be qualified as popular history at best. The best book I've found on the subject is Real NASCAR: White Lightning, Red Clay, and Big Bill France by Daniel S. Pierce (Chapel Hill: University of North Carolina Press, 2010).