A private prison is a prison run by a private company instead of the government. The government hires the private prison company to perform all the services needed to keep the convicts locked up while they serve out their sentences.
In the twenty-first century, many industries that were government-run before have become more privatized. This means that making money is the top priority of the organization. So when you commit a murder or a rape and are convicted, you are benefiting the prison company's shareholders. You are helping create jobs.