To bring forth what did not exist before. The same root as kin and kind - to generate is to beget.
Latin generare (to beget, produce), from genus (birth, kind, race), the same root that gives kin and kind; to generate is, at root, to beget.
Making something that was not there a moment before is treated as a kind of birth rather than a kind of construction, in the same word family that gives kin and kind.