In plain words
When she saw Lakṣmaṇa and Śatrughna stop crying and play happily, Sumitrā's mind was at peace. When she found Vasiṣṭha alone, she went to him again and asked him to tell her the reason for her children's strange behaviour. Then Vasiṣṭha: “Sumitrā! You are a woman of virtue, rich in good conduct. Your mind is pure, steady and selfless. So you can grasp this easily. That day, when a kite snatched away your bowl of pāyasa, Kausalyā and Kaikeyī each gave you half of their pāyasa, did they not! Lakṣmaṇa is the very one born of the pāyasa Kausalyā gave. Śatrughna is the very one born of the pāyasa Kaikeyī gave. So Lakṣmaṇa is of Rāma's portion, and Śatrughna is of Bharata's portion. Because each portion has joined its own, they are happy,” he explained. Kṛṣṇa too said this very thing in the Bhagavad Gītā: “Mamaivāṃśo jīvaloke jīvabhūtas sanātanaḥ.” “All are nothing but portions of Me,” He said.
Rāma, Lakṣmaṇa, Bharata and Śatrughna came of age. Daśaratha resolved to have them married. At that very moment a messenger came in: “Great king! The revered Viśvāmitra has arrived,” he announced. By the will of God, whatever must happen at a given time happens then. Daśaratha himself went to the gate in person and welcomed Viśvāmitra. “Swami! My good fortune has ripened. This very day I resolved to have my sons married. And now your blessing too has come to me. Your coming gives me great joy. I ask you to tell me the purpose for which you have come. Whatever help you need, I am ready to give it,” he said. Then Viśvāmitra said that he had undertaken a yajña, and that he had come for Rāma, to take Him along and guard that yajña so that no disruption would come to it from the demons. It was as if a great atom bomb had fallen into Daśaratha's heart. “I had these children only after performing yajñas and yāgas for a long time.