In plain words
Kaikeyī too poured half of her pāyasa into Sumitrā's bowl. See what great fruit that harmony bore! It was because they lived in harmony that they won God's grace. To Kausalyā Rāma was born. To Kaikeyī Bharata was born. But to Sumitrā two sons were born. Why? Because of the pāyasa she took, half was Kausalyā's and half was Kaikeyī's. Those two halves took shape as two forms. The two were named Lakṣmaṇa and Śatrughna.
Since he came from Kausalyā's pāyasa, Lakṣmaṇa was always at Rāma's side. Since he was born of the pāyasa Kaikeyī gave, Śatrughna was always at Bharata's side. “Ah! If Rāma rules the kingdom, Lakṣmaṇa will be his minister and help him. If Bharata rules the kingdom, Śatrughna will be his minister and help him”: so Sumitrā rejoiced. Because she was a good friend to all, the name ‘Sumitrā’, good friend, was true of her. When Kausalyā was grieving that Rāma was going to the forest, Sumitrā went to her: “Sister! Why are you grieving? Who do you think Rāma is? He is no ordinary man; he is God Himself. No harm of any kind will come to him”, and so she gave her courage and consoled her. It was only because Sumitrā gave her courage that Kausalyā was able to stay on in Ayodhyā; otherwise she too would have gone to the forest with Rāma.
And the kite that had snatched away Sumitrā's bowl of pāyasa let it fall on a hill before Añjanādevī, who was there in meditation. Añjanādevī ate that pāyasa, and Hanumān was born of her womb. That is why Rāma and Lakṣmaṇa came to be friends with Hanumān, and Hanumān lifted the two of them on his shoulders, carried them up the Ṛṣyamūka hill and presented them to Sugrīva. From then on they would never leave one another. See how much strength harmony gave in this way! Unity is great strength. If you do not speak to one another and keep up enmity, you will achieve nothing.