The cadent houses are the third, sixth, ninth and twelfth, each falling away from an angle. The Greek word is apoklimata, the declining places, and the Latin cadens, from which the English word descends, means falling. Both names describe one geometry: these are the houses a rising sign has just passed through on its way down from a pivot.
The tradition counts a planet here weakest. It is the accidental debility that matters most in traditional judgement, and it is why an otherwise dignified planet can produce very little. A benefic in its own sign but in the twelfth is a good thing in a place from which it can barely act. The doctrine runs consistently from Hellenistic practice through to Lilly and is applied without much softening.
Weakness is not the same as unimportance, and the subjects of the four make that clear. The third holds siblings, neighbours and elementary learning. The sixth holds illness, servants and daily work. The ninth holds religion, philosophy, long travel and dreams. The twelfth holds imprisonment, hidden enemies and self undoing. Those are four of the most consequential regions of a life, and the tradition assigns them to the four weakest houses without evident discomfort.
All four carry planetary joys: the Moon in the third, Mars in the sixth, the Sun in the ninth, and Saturn in the twelfth.
Sources The Daimon in Hellenistic Astrology: Origins and InfluenceDorian Gieseler Greenbaum with Christian AstrologyWilliam Lilly