A private security guard is someone who works in the private sector, as opposed to the public sector. Public sector security personnel might work with the police or the army, whereas a private security guard is more likely to work in the corporate sector, or in commercial spaces. If you are looking for work that will make you more money and give you more freedom, private security work is a good option.
You can find work with a private firm, or you can choose to work for an agency. If you have a specialist skill or lots of experience, it might also be possible to work for yourself as a standalone security guard. Usually, people who do this a security dog handlers, or specialist security guards for sectors such as events and corporate guarding. The best option is usually to start out with an agency, then make a name for yourself in the industry.