The river teaches Siddhartha how to listen.  In the river, Siddhartha, now an old man, hears his own father and son, and they flow together; he hears Kamala and Govinda, and all of them flow into one another and over each other, all becoming the river, all making up the river's voice.  Siddhartha becomes "Nothing but listener now," and he can't distinguish between the many voices in the river anymore.  The more he listens, he hears that the happy and the sad, the raging and the hurting, are all one: "everything was one, everything was interwoven and intricately knotted, a thousandfold."  He hears everything, altogether, and this sound is the world in its perfect unity.  He hears "OM: perfection."  Once the river teaches Siddhartha to listen, to hear OM, his pain joins with it, and he stops struggling with his fate and he stops suffering.  At this point, now that Siddhartha has achieved enlightenment and an understanding of OM, his friend Vasudeva leaves him.

Siddhartha has many teachers that he learns from on his journey towards Enlightenment, but ultimately, it is the river that teaches him the final lesson that he needs to learn in order to attain his goal. As Siddhartha listens to the river at Vasudeva's urging he realises that the river symbolically represents life itself as is shown through the sounds that Siddhartha hears emerging from the river, representing the sound of all of creation. In this river, Siddhartha learns that all of creation is absorbed into one harmonious whole. Note how the text presents Siddhartha after this epiphany:

From that hour Siddhartha ceased to fight against his destiny. There shone in his face the serenity of knowledge, of one who is no longer confronted with the conflict of desires, who has found salvation, who is in harmony with the stream of events, with the stream of life, full of sympathy and compassion, surrending himself to the stream, belonging to the unity of all things.

Siddhartha therefore learns that he is one life that is part of a united whole and that part of Enlightenment consists in the act of surrender. This is shown by Siddhartha's acceptance of his destiny and his surrendering of his conflicting desires. Ultimately, he learns to surrender himself to the flow of the stream and to accept what his destiny has for him.