In plain words
Merely because He plays, sings and walks about in this way with people of the world, the powers of that supreme stage are not lost anywhere. But only to people of small understanding does all this look different. Rāma grieving like an ordinary man, being shaken when separation befalls Him, and such things are seen a great deal in the Rāmāyaṇa. But if you ask why Rāma did all this: He kept displaying it in this way to teach His fellow men a natural devotion to Dharma, and to give them an ideal of how each person should behave.
Keeping a father's word; the giving up of Sītā
The Rāmāyaṇa is the great poem that has given every home, every family, the ideal it needs most. The story of Rāma is what teaches how father and sons, wife and husband, brothers, king and subjects, the wives of brothers and others like them should conduct themselves. This principle of the Avatāra is just what fostered oneness in every home in this way, granted divinity and turned it into God's own nature. Rāma was ready to fulfil the word Daśaratha had given long before to His stepmother. At the very moment He could have become king, He gave up so sacred an opportunity and went to the forest. Rāma, all-knowing, all-pervading, all-powerful, was fully able to rule the kingdom. Though He had such complete ability, He gave up everything He had to uphold His father's word, and went to the forest. This is an ideal deed. Rāma upheld the truth that the line of Ikṣvāku had won renown for keeping a father's word. To uphold that truth, however many hardships and however many losses came, Rāma bore them, endured them, withstood them, pushed through them and went on ahead.
He went on following all these different ways so that the people's love and trust would grow. When a lowly washerman cast some groundless “slander” on Rāma, He thought, “If even a lowly man among my people torments me with such words, how deeply this secret must lie hidden among the rest of my people!” and, so that the world would recognise the real truth, He could bring Himself to send Sītā to the forest. That is precisely why Śrī Rāmacandra became a great king of high renown in ruling his people.
Today the incompetent and the incapable stand ready to rule the people, and they covet it. This is sheer wickedness. This above all is the reason Bhārata today has sunk to so sorry a state. The rule of the incompetent is the very thing that has dragged Bhārata lower still. To rule the people, holy men must come forward who are virtuous and able to give up self-interest. Śrī Rāma is the very one who showed forth this ideal. This emperor was one who clearly recognised the close bond of kinship between the people and Himself, and lived by it.
The love between brothers
The unity and the affection of Rāmacandra and His brothers are beyond description. At His stepmother's command Rāma might put on bark garments, take the guise of an ascetic and go to the forest; but Lakṣmaṇa was under no one's command, and had no need to follow anyone.