a group that belongs together by common origin: offspring, a people, or a kind of thing
At heart this word gathers things that share a common source. It comes from the same family as the verb "to be born" or "to come into being", so it names whatever has been produced from one origin. That single idea stretches a long way: from one person's child up to a whole nation, and even to a class of things that share one nature.
When it points to people, the scale slides. It can mean a single descendant or a whole line of them (the "offspring" of David, or humanity as the children of God), then a family or stock traced back to one forebear, then a whole people or race. English has to switch words as the scale grows (offspring, family, stock, race, nation, countrymen), but the Greek stays one word throughout. It sits close to γενεά, "a generation", and overlaps the everyday word for a nation, ἔθνος, without being either.
The same word also sorts non-human things into types. Fishermen haul up "every kind" of fish, Paul lists "kinds" of tongues, and Jesus speaks of a "kind" of spirit that comes out only by prayer. Here it means a class whose members belong together because they share a common nature.