Plot in The Odyssey
Zeus has been reminded by Athena that Odysseus is stranded on Calypso's island. Zeus states that he has not forgotten Odysseus, but that Poseidon is still enraged for Odysseus's blinding of Polyphemus the Cyclops. In an effort to get Odysseus home, Zeus agrees that all the gods and goddesses should find a plan to convince Poseidon to cease his vendetta.
Odysseus' father. With Odysseus away, Laertes should've taken over his house, as the eldest male in the family, but the narrative requires that no strong figure be present in the household, and thus, Homer made Laertes old and feeble so he wouldn't be able to fulfill his duties to Odysseus. Athena mentions this as a way of commenting on the confluence of bad luck that led to this situation with the suitors.
Odysseus' house and possessions are reflections of his great social standing, with items like this ewer, or oval pitcher, displaying his considerable wealth and prestige. Even before Odysseus fought in the Trojan War, he was a respectable man with lands and money to his name. His absence, however, has depleted his wealth considerably, as the suitors eat up his flock.
The god of the sea, also known as the "Earth-Shaker" because of his ability to cause earthquakes and tidal waves. He hates Odysseus for blinding one of his sons, the Cyclops named Polyphemus. This story is recounted later in the epic poem and is one of many tales Homer foreshadows in these passages.
Modern readers will recognize this as a stalling tactic used by someone with a reason to believe that a straightforward rejection would result in some backlash or violence. Penelope's "artful" scheme is in reality a way to hold off making her decision about remarrying in the hopes that Odysseus will come save her from the suitors. It remains to be seen if he'll make it back in time.
Following Agamemnon's murder, his estate would've fallen into the hands of Aegisthus and Clytemnestra, then passed again to Orestes, Agamemnon's son, after he avenged his father. Traditionally, Menelaus would've become King of those lands in his brother's wake, but since he was away, he wasn't able to claim his rights in the matter.
Odysseus's men are, understandably, not happy with this turn of events. Groaning, tearing one's hair, and even tearing one's clothes were common customs of mourning and distress during ancient times.
Note that Athena's plan is to have Odysseus hide within a disguise she provides for him; this is somewhat similar to and builds on his idea for the Trojan Horse from the Iliad. Both deceptions conceal what is underneath, and both lead directly to many deaths.
This is the second time Athena has interceded on Odysseus's behalf by making him less visible in order to protect him; the first time was during his walk to Alcinous's cloister. Notice how Homer is attributing these circumstances to the gods while simultaneously using them as a device for controlling the elements of the plot.
This story will seem familiar to readers: it's been mentioned before by Odysseus in the story he told Alcinous and his men. Here, we see a somewhat more elaborated version, which may suggest that the exact details of the story were so well-known in Greece that Homer needn't relate the whole thing to his audience.
Notice how Athena performed similar enhancements on Odysseus’s body. This reflects what types of bodies Homer considers heroic. Odysseus is visually a classical hero, and Penelope’s unwavering devotion to her husband is now reflected in her looks. Homer links one’s strength of character with their outward appearance.
It's highly unlikely that these women, many of which are called maids, would be old enough for him to remember all of them, since he's been gone for twenty years. It's also somewhat unlikely that they would want to embrace him when he's covered in blood, but Homer overlooks this to make Odysseus seem like a beloved king.
Remember that Telemachus removed all weapons from the walls earlier in the poem and that the suitors are now left only with what they have on them: their own swords, perhaps a few spears, and no shields whatsoever. If they'd been less arrogant, perhaps they would've been prepared for this attack.
Even though he is reunited with his wife and in Ithaca, Odysseus still has to repay his debt to Poseidon, as Teiresias had foretold, to finally be able to live out the rest of his life in peace.
Remember, however, that a prophecy has foretold that Odysseus will have to leave Ithaca to make offerings to the gods and appease them for all of these deaths. It's unclear whether Athena's actions have made that journey unnecessary. Either way, the poet makes a point of ending on a peace treaty to resolve any lingering tensions in the poem.
Most likely, a caduceus, a staff carried by Hermes and other heralds that gave the appearance of two snakes intertwining. Today, the caduceus is commonly associated with the practice of medicine, and its symbol is warn by doctors and professionals as a sign of their devotion to healing people.