There, awaiting my morning grumble, in the middle of an Associated Press article on the recent tornadoes: "crews recovered pieces of peoples' lives."
People, a plural noun, is equivalent to "human beings" or "persons."
Peoples, a plural noun, identifies a group of human beings, typically a large one, with a common culture or kinship.
Crews were therefore recovering people's effects, the belongings of individuals.
Unless you are writing about the peoples of the world represented at the United Nations, you are seldom going to be called upon to use anything but people.
See if the Associated Press can master this distinction, and if it sticks, maybe tomorrow it can have a go at another one.