First the red and yellow. The exact meaning of the colors are still being argued about but the oldest legend says that the red represent the king's blood and the yellow represents his gold shield. So it mean the king's blood in his gold shield. The yellow band in the middle of the red is about 2 times the size of the red bands because the coat of arms is on the yellow band.
Now the coat of arms. It's the design on the yellow band. Crown: Kingdom of spain. Castel: king of Castilla. Lion: Kingdom of Leon. Pallet Gules: kingdoms of Aragon. Chains: Kingdom of Navarra., Fleurs de lis: Royal