We use the possessive form of people when we want to show that one group of people owns something. People’s phones are always making loud noises on the train. We are part of the people’s movement.

We can use possessive 's to talk about the relationship between people or to say who owns something. Possessive 's always comes after a noun or a name. We often use possessive 's or s' when we talk about family and friends. Grandma and Grandpa are my mum's parents. Maria's best friend is Juanita. My cousins' birthdays are both in January.

People’s is the plural possessive of the word person. E.g., “People’s lives are more difficult due to austerity.” Furthermore, the term peoples’ can be correct to refer to groups of people possessing things, but it is not common. E.g., “The government neglected the indigenous peoples’ demands.”

The people’s choice is clear in this election. (What the group, as a whole, prefers) The people’s park is open from dawn till dusk. (The park belonging to the community) The people’s representative speaks on their behalf. (The representative of the populace)