This quote is taken from Book IX, lines 7-9; Odysseus acknowledges that he is widely known by mortals and gods both, and he is admired and respected for his intelligence and many skills.
At this point Odysseus is the only remaining member of the contingency that he took to Troy. He has spent eighteen days at sea after parting from Calypso and heads toward Scheria, the island of the Phaeacians. But, Poseidon, who hates Odysseus because of what he has done to his son the Cyclops, has been angered at the help the other gods have given Odysseus. So, he creates a maelstrom that nearly drags Odysseus under the sea. Fortunately, he is rescued again by the goddess Ino. Odysseus continues until he finds a river where he can swim into its waters. He walks onto the shore and rests in a covered area.
The next day, the Phaeacian Princess Nausica discovers Odysseus while she and her handmaidens wait for their clothes to dry. She provides him clothes and has Odysseus walk alone to the palace and instructs him on what to say when he arrives.
Book IX, then, relates the time that Odysseus is a guest of the Phaeacian king and queen, Alcinous and Arete. Alcinous calls an assembly that votes to provide their foreign guest with a ship so that he can return home.
Later, there is a feast and games in honor of the guest, but when Odysseus hears a bard sing of the "quarrel" between Odysseus and Achilles at Troy, he is overcome with sorrow, and he weeps. Nevertheless, at dinner Odysseus asks the bard to sing his song again about Odysseus at Troy, and once again, he cries. So, King Alcinous has the music stopped. Further, after the celebratory games, he asks Odysseus to reveal his identity. Odysseus does, and then he is asked to reveal where he is from and where he wants to go. He begins,
"I am Laertes's son Odysseus. Men hold me formidable for guile in peace and war: this fame has gone abroad to the sky's rim."