You must be referring to the passage in book eight, near verse 75. The passage is rendered as follows in Butler’s translation:
“The company then laid their hands upon the good things that were before them, but as soon as they had had enough to eat and drink, the muse inspired Demodocus to sing the feats of heroes, and more especially a matter that was then in the mouths of all men, to wit, the quarrel between Ulysses and Achilles, and the fierce words that they heaped on one another as they sat together at a banquet. But Agamemnon was glad when he heard his chieftains quarrelling with one another, for Apollo had foretold him this at Pytho when he crossed the stone floor to consult the oracle. Here was the beginning of the evil that by the will of Jove fell both upon Danaans and Trojans. Thus sang the bard, but Ulysses drew his purple mantle over his head and covered his face, for he was ashamed to let the Phæacians see that he was weeping.”
(Cited from Wikisource, emphasis is mine; Ulysses is the Latin variant of
In the dutch translation by Patrick Lateur, the translator says in a note to verse 75: “on this theme, nothing else is known. Perhaps we are dealing with an improvisation by Demodocus. The fact that Odysseus is the subject of the song is not without significance. He is given a special place opposite Achilles, a position he did not even have in the Iliad.” (Source: Homeros. Odyssee: een zwerver komt thuis. Athenaeum—Polak & Van Gennep, Amsterdam, 2016, p. 525.)
Gregory Nagy expresses another opinion in the third chapter of his book The Best of the Achaeans (1999, revised edition, accessible online). He argues the enmity between Achilles and Odysseus might have been a stock epic theme, to which (subtle) hints can be found in several scenes of the Iliad. What was the fight about? Nagy says: “The contrast apparently took the form of a quarrel between the two heroes over whether Troy would be taken by might or by artifice.” (Here, “might”/force is connected with Achilles and “artifice”/stratagems with Odysseus.) You might be interested to read the whole chapter here.