There is confusion about the best way to describe more than one person. It often feels better to speak of "three people" rather than "three persons", but this suggests that people is the plural of person.
The words people and person derive from different Latin roots, the former from populum, referring to the people in the sense of the populace, the latter from persona, "an actor's mask; a character in a play" and which in the English form person came to refer to an individual human being. (It was first brought in via French in the form parson, which for some unexplained reason soon took on the separate and specific sense in which we still use it, so that the word had to be re-borrowed with a new spelling. And persona itself was borrowed in that form by Jungian psychologists early this century to identify the personality a person presents to the world.)
The normal plural of person was persons, as in "two persons were present". However, there is evidence from Chaucer onwards that some writers chose to use people as a plural for person, not only in the generalized sense of "an uncountable or indistinct mass of individuals" but also in specific countable cases (Chaucer wrote of "a thousand people"). This began to be questioned in Victorian times, and the pseudo-rule grew up that the plural of person is persons when a specific, countable number of individuals is meant, but that people should be used when the number is large or indefinite.
Modern style guides disagree, being able to quote many examples of the use of people as the plural of person in both situations, for example in sentences like "the plane crash killed 370 people", and "Many people visit the park every day". Though persons survives, it does so largely in formal or legal contexts ("Killed by person or persons unknown", "This taxi is licensed to hold four persons") and often seems awkward and old-fashioned. Where it survives it emphasizes that each member of a group is being considered as an individual: "The nearest persons they can vent their feelings on are the ball boys and girls", "Eight persons shared a single room". From the evidence, it seems that the trend towards using people instead of persons is accelerating and that it may not be so long before persons vanishes from the language except in certain set phrases.
The reverse process seems to be happening with people. Though in origin it is a singular collective noun, it has almost from the earliest times been treated as a plural term for people at large (which has no doubt aided its acceptance as the plural form of person). This has now become so commonplace, as in usages like "People are always looking for a bargain" or "The people are being asked to vote in a referendum", that now the singular form of people seems even stranger than the plural form of person: "This people is angry", "That Aboriginal people has died out".
The plural form peoples logically refers to more than one community or nation, although down the centuries some writers have been chary of it, and in the nineteenth century one described its use as "uncouth". These days it is the accepted form in contexts like "His authority shaped diverse peoples into common views and allegiances" or "Magnified traditions especially bolster peoples embittered by subjugation or newly come to nationhood".