A person is a human man, woman, or child.

It is a singular countable noun.

There was one person at the door.

The plural of person is people.

It refers to a group or a number of human beings.

It is a plural countable noun.

There were three people at the door.

So how about persons?

Persons is a plural countable noun.

It's similar to people, but it's considered more polite and more formal.

It's most often seen written down.

This lift can hold a maximum of 15 persons.

And peoples?

Peoples is the countable plural form of people and comes from the other meaning of people.

People can mean nation.

The Aztecs were a people that lived in the Americas.

Or, there are many peoples living on the Earth.

They are all human - so far.