Which word is correct and what is the difference between these words?
I heard somebody say that "people's does not work in a sentence. People means a group of humans. Why would you make the word plural again?"
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People is a collective noun. When we talk about a specific group of people, we consider it as singular and therefore, no need to add s.
Peoples is used when we talk about two or more different ethnic groups. For example, "All the 14 distinct peoples (native groups) of the continent were part of the survey".
Whereas People's is not the plural form. The apostrophe ('s) is used to indicate possession.
The box is mine.
The box is hers.
The box is theirs.
The box is my family's.
The box is the people's. (The box belongs to the people.)
Likewise, the People's President means the President of the People.
Actually, I think you are looking for the difference between people and peoples.
People means indeed a group of humans, as in:
The people of Germany speak German.
It can also be used as a plural of person:
Many people like apple pie.
The plural of people is peoples and is used when you talk about several groups of humans, usually several ethnic groups:
The peoples of Asia are vary varied.
It is not used very often, so usually you will use the singular.
Note You asked about people's, but that is not the plural form (you also wrote human's when you meant humans.
The apostrophe is used to indicate the genitive (possessive) form:
John's book -> the book that belongs to John.
You could certainly use people's in a sentence:
The elections showed the people's wish for change.
The wish belongs to the people. In this sentence, people means all the humans that live in the country we are talking about (where elections were held).