Sankin means that daimyo served for the lord (Seii-Taishogun [literally, "great general who subdues the barbarians] in this case) for a certain period, while kotai means that they returned to their domains on leave to attend to government affairs there.
参勤は一定期間主君（この場合は征夷大将軍）のもとに出仕すること、交代は暇を与えられて領地に帰り政務を執ることを意味する。