Private placements fall under Regulation D, usually, which stipulates the rules by which investors can be sought and placed into privately arranged contracts for equity investments.
Private placements may be for non-public companies, or it may be a private offering of a publicly traded company. Regulation D stipulates the guidelines by which investors can engage in private investment without many reporting requirements.
People who have committed felonies cannot be part of private placements, which falls under the Bad Actor rule. Most investors will need to be Accredited Investors in order to be able to invest in a private placement, but if there are under 35 non-accredited investors, it may be acceptable to the SEC.
Private placements may be for specific projects, such as movies being made in your state, or for the ownership of equity in small businesses that are not publicly traded. There are also sometimes privately-placed equity arrangements from publicly traded companies, who want to raise capital by offering shares to specific investors or entities, and they usually price these shares at a discount.
If the company is publicly traded they need to register the offering with the SEC, but for the most part these arrangements have no registration requirements with the SEC. Investment advisors and the company offering the private placement may solicit sales from a few accredited investors, especially through referrals, but they cannot advertise the offering in order to abide by Regulation D.
Investors are generally going to be limited partners who do not have control over anything once they buy into the venture.