In the Book 16 of Homer's Odyssey, the title character has returned to his native land of Ithaca after 20 years of warfare and wandering. Disguised as a beggar, Odysseus has stayed in the hut of his faithful swineherd Eumaeus since his return. While staying with Eumaeus, Odysseus' son Telemachus, who has been searching for his father, comes to Eumaeus' hut.
Initially, Odysseus appears as a beggar to Telemachus. After Telemachus sends Eumaeus off to inform his mother Penelope of his return, Odysseus (with an assist from Athene) reveals his true identity to Telemachus, who was a baby when his father left for Troy.
When Telemachus realizes that the man standing before him is his father, the two men experience a tearful, but joyful reunion. Homer's simile runs as follows:
They keened aloud, and their cries rose, louder and more frequent than those of birds of prey with curved talons, vultures or sea-eagles, whose nests have been robbed of their unfledged chicks by country folk. (A.S. Kline translation)
Thus, we experience one of the most emotional and touching scenes in this epic poem as father and son come together for the first time in Telemachus' adult life.
The simile is found here:
So saying, he sat down, and Telemachus, flinging his arms about his noble father, wept and shed tears, and in the hearts of both arose a longing for lamentation. And they wailed aloud more vehemently than birds, sea-eagles, or vultures with crooked talons, whose young the country-folk have taken from their nest before they were fledged; even so piteously did they let tears fall from beneath their brows. And now would the light of the sun have gone down upon their weeping, had not Telemachus spoken to his father suddenly: “In what manner of ship, dear father, have sailors now brought thee hither to Ithaca? Who did they declare themselves to be? For nowise, methinks, didst thou come hither on foot.”
Perhaps if this specific simile were not used to describe this reunion, it would have been far less impactful for the reader. Their cries and weeping are likened to the sounds of birds who cry loudly and grieve over the loss of their loved ones. So we know that the reunion is a very emotional one that is both an occasion of happiness and also one of sadness. We can tell that Telemachus and Odysseus have suffered much and have been subjected to much unfairness. Their reaction upon meeting one another again is definitely an outcry of these experiences.