Poseidon, the god of the sea, pursues Odysseus because he blinded the Cyclops Polyphemus, who is the god's son. In the council of the gods in the first book, Zeus explains to Athena that it is Poseidon who pursues him: the god does not kill him, but "makes him wander far from his homeland." That is why Odysseus takes so many years to return, even after the war had ended.
The origin lies in Polyphemus's cave, narrated by Odysseus in Book IX. The Cyclops devoured his companions, and Odysseus made him drunk and drove a stake into his eye. Already from afar, instead of sailing off in silence, Odysseus shouts his true name and the house where he lives, and Polyphemus, blind, raises his hands to Poseidon: "if I am truly yours," he prays that Odysseus not reach his home or, if fate allows it, that he "arrive late and in misery, having lost all his companions, in a stranger's ship, and find troubles in his house."
The curse comes true point by point. Poseidon, who was far away at a banquet among the Ethiopians, returns, sees Odysseus's raft near the Solymi mountains, and unleashes a storm that destroys it. Later, when the Phaeacians carry him home, the god complains to Zeus that mortals do not honor him and turns their ship to stone in view of the city. Even Athena, Odysseus's protector, avoids appearing to him on the journey, out of respect for her uncle, until he sets foot on his native land.
What limits Poseidon's anger is Zeus's will. The poem makes it clear that the return is part of Odysseus's fate, and Poseidon cannot deny it; he can only delay it and make it costly. That is why the punishment takes the form of a long detour and not of a death. The Phaeacians, who descend from Poseidon himself, help all shipwrecked men return home, and King Alcinous's father had already warned that the god was angered by these escorts that do no harm: it is the same anger, seen from the other side.