Origins
A kingdom is the judgement-realm of the kinsman — and every syllable of that definition maps to the word's actual etymology. Old English cyningdōm breaks into cyning ('king') and -dōm ('jurisdiction, realm').
The word king itself traces to Proto-Germanic *kuningaz, probably from *kunją ('kin, family'). A king was 'the one of the kin' — the man who represented the tribe, chosen from among the family. This makes king a cousin of kin, kind, and kindred.
The suffix -dom comes from Proto-Germanic *dōmaz, meaning 'judgement' or 'decree'. It is the same word as doom, which originally carried no sense of catastrophe. Old English dōm meant 'judgement, law, authority'. Doomsday was simply Judgement Day. The suffix survives in freedom (the state of being free), wisdom (the state of being wise), and even boredom.
Figurative Development
Kingdom entered English before the 10th century and has changed remarkably little. The biological use — animal kingdom, plant kingdom — dates to the 17th century, when Carl Linnaeus borrowed it to classify the natural world. The metaphorical use ('the kingdom of the mind') is older still.
German chose a different compound: Königreich uses Reich ('realm') rather than -tum (the German cognate of -dom). But Dutch koninkrijk and the Scandinavian forms preserve the same structure as English.