In many court cases a prosecution means the government brings charges on behalf of the community. That idea comes from the old legal word *sovereign*, which simply means the person or group who speaks for everyone. So when a case says "People v. Someone," it means the court is hearing a complaint brought for the public good.
Different places use different words for the same idea. For example, some U.S. states write "the People" in case titles—California, Illinois, and New York do this. Other states put the state's name, and four call themselves the "Commonwealth" (Massachusetts, Virginia, Pennsylvania, Kentucky). Outside the U.S., Ireland and the Philippines also bring cases in the name of the people, while the United Kingdom uses the "Crown." Some countries add words like "People's Republic" to show a particular type of government.