As I child I never thought too much about why the plural of person is people. It was just one of those quirky English things, like geese, or children. Then I started hearing the word persons, and thought how pretentious and silly it sounded. But an etymological search reveals a funny thing: person and people are etymologically totally unrelated. I can't think of any other English word in which the singular and plural forms are actually not the same word at all. Can you?
Let's start with people. The Latin word for humans in general was populus, from which we get popular, populate, and population. Public, republic, and publish are also related, coming to us from another Latin form of the word. We get the form people from alterations the Latin word experienced while coming to us by way of French.
As for person, our word comes ultimately from the Latin word for an actor's mask, with the roots meaning "sound through," because of the way the actor spoke through the mouth hole. Yep, it gives new meaning to the idea that we're all just actors wearing masks in the face of the world! We also have the word persona, which is closer to that original idea, but which wasn't introduced until the twentieth century. The same Latin (and possibly Etruscan) root gave us parson, and, more obviously, personality.
Technically, going by the roots, people would be the correct plural for a group of humans when the emphasis is on the group, while persons would be the plural for a collection of specific individuals. And some people do try to make this distinction in their rules on usage. But in my experience people is simply the normal, everyday plural in any situation, while persons is the plural used in legal and official contexts.
So that's taken care of - but if you think English's variety of person words ends there… oh no. Of course not. Just to round out our look at words for people, Latin had other words for humans. The word meaning "being of earth" (as distinct from the gods) was humanus, from which (by way of Old French) we get human and such related words as humane and humanity. The Latin word denoting the common people was plebs. From this root we get, naturally, plebeian. This may be related to the Greek word pléthos, meaning "multitude," from which derives our plethora. And ancient Greek had another word for the people living in a particular district: demos. When they participate in government we get a democracy, hopefully of the people, by the people, for the people.
[Picture: Intertwined, rubber block print by AEGN, 2003.]