What xenia is
Xenia is usually translated guest-friendship, and it is not politeness. It is a reciprocal institution with divine sanction, binding on both parties and heritable between families, governing how strangers are received in a world with no other mechanism for safe movement between communities. Zeus in this aspect is Zeus Xeinios, the protector of guests and suppliants.
The Greek word xenos means both guest and host, and also stranger. That the same noun covers all three is the concept in miniature: the relationship, not the person, is what is named.
The sequence
The poem knows a fixed order and expects the audience to know it too: receive the stranger, seat him, wash him, feed him, and only then ask who he is. Asking first is a discourtesy, because it makes the welcome conditional.
Departure has its own obligations: a guest-gift, and where possible conveyance onward. The Phaeacians uniquely provide pompē, escort all the way home, and it is what finally ends the wandering.
The poem as a series of tests
Almost every episode is a variation on the pattern.
Performed perfectly. The Phaeacians, who receive an unnamed naked stranger, feed him, entertain him, give him gifts and take him home. Nestor and Menelaus, who feed Telemachus before asking his name.
Performed by the poor. Eumaeus the swineherd, a slave, who gives what he has and states the principle explicitly: all strangers and beggars are from Zeus, and a small gift given kindly is a gift.
Distorted into detention. Circe and Calypso, where hospitality becomes captivity and the guest cannot leave.
Inverted entirely. Polyphemus, who asks who they are before feeding them, cares nothing for Zeus, and announces that his guest-gift will be to eat Nobody last.
Violated from the inside. The suitors, who are guests consuming their host's substance. This is the poem's most sophisticated case, because they have not broken in; they were admitted, and they abuse the position.
The political meaning
Xenia is how a world without states manages the movement of people. The Cyclopes are described as having no assemblies and no established rights, and it is in that context that Polyphemus eats his guests: the absence of hospitality and the absence of institutions are the same fact.
This is why the killing of the suitors is presented as just rather than as vengeance. Their offence is not desiring Penelope; it is consuming a household while enjoying its protection, and doing so against warnings. Under the poem's terms they have attacked the only institution holding the society together, and Zeus's protection of guests is also, in the end, a protection of hosts.
The ethical tension
The poem's own standard is applied unevenly, and it does not hide this. Odysseus sacks the city of the Cicones on his way home from Troy, which is not treated as a breach of anything. He enters the Cyclops's cave uninvited, eats the cheese, and stays to see what gift he will be given. Hospitality in the Odyssey is a real obligation and also a resource the clever exploit.
Later interpretation
The concept passed into Greek political thought as a model of obligation to the outsider, and into Roman practice as hospitium. It remains the standard example in modern classical scholarship of a moral institution carried entirely by custom and religion rather than by law.