Left person radical - the side-stacking variant of 人. Anchors 健 in human-quality words alongside 佳 (fine), 优 (excellent), 俊 (handsome). Marks the strength/health described as a property of a person, not a thing - a body that holds itself up well.
Right 建 supplies the sound jiàn exactly and adds a useful semantic flavour: a person who is solidly built, well-constructed, soundly established in body. Same phonetic family: 键 (key), 腱 (tendon), 毽 (shuttlecock). All share the perfect jiàn rime.