Dictionary.com provides quite a few definitions for people, most relevantly:
- persons indefinitely or collectively; persons in general
- the entire body of persons who constitute a community, tribe, nation, or other group by virtue of a common culture, history, religion, or the like
Looking at the first definition, you would say something like "they are good people" when referring to any collection of individual human beings (without necessarily a common trait).
For the second definition, note that there can be multiple such bodies of persons that constitute a set group (sorted by nationality, culture, religion, etc.); take for example citizens of Wakanda and citizens of Asgard. If you want to refer specifically to the Asgardians, you would say "The Asgardians are a people", distinct from every other group of people. I guess you could say there is an implied sense of unity in saying something like "the Asgardian people" or "we (the citizens of Wakanda) are a good people".
Saying "a people" is not an old style of English, nor merely a different way of saying "people". It does indeed give another meaning to the sentence by grouping certain people by a common trait.