The word
Nostos is the return home, and it gave us nostalgia — literally the pain of the return, a coinage of the seventeenth century rather than a Greek word. In Homeric usage it names both the act of getting back and a whole class of stories: the returns of the Achaeans from Troy, of which the Odyssey is one and the murder of Agamemnon another.
The Greek category is important because it is not sentimental. A nostos is a completed journey with a successful arrival, and the poem is full of returns that fail. The men who died at sea did not have one; Agamemnon, who arrived and was murdered at dinner, is the poem's standing example that arriving is not sufficient.
What it costs
The Odyssey fixes the value of homecoming by making it expensive. Calypso offers immortality and eternal youth, in a beautiful place, without conditions. Odysseus refuses, saying he knows his wife is lesser than a goddess to look at and that he wants his return regardless, through further suffering if necessary.
That refusal is the poem's central assertion. Being mortal, in a particular place, with particular people, is worth more than being a god somewhere else. Everything that follows — twenty years, a drowned crew, a massacre, a marriage bed rooted in the ground — is the working out of a decision made on a beach in Book 5.
Arrival is not restoration
The poem is careful to separate three things that adaptations tend to collapse.
Arrival. Odysseus lands on Ithaca in Book 13, asleep, and does not recognise it. Eleven books remain.
Recognition. He has to be identified — by a nurse, a dog, two herdsmen, a son, and finally by his wife on her own terms in Book 23. Getting home is not the same as being known to be home.
Restoration. The suitors have to be dealt with, and dealing with them creates a blood feud that Athena has to suppress by force in the last hundred lines. The house is recovered; the community is only pacified.
The unfinished return
Tiresias's prophecy in Book 11 puts a further journey after the poem ends: Odysseus must travel inland carrying an oar until he meets people who take it for a winnowing fan, sacrifice there to Poseidon, and come home to a gentle death from the sea in prosperous old age.
The Odyssey therefore does not end with the homecoming complete. The sea-god is still owed. This is the detail that makes the poem's treatment of return serious rather than consoling, and it is almost always cut.
Later interpretation
The nostos pattern became one of the most durable structures in European literature — Virgil inverts it into a foundation story where the hero must not go home, and Joyce transposes it onto a single day in Dublin. Dante and Tennyson took the opposite path and made Odysseus a man who cannot stay, which is a reading of the further journey rather than of the poem.