The Odyssey by Homer is an epic poem that tells the story of Odysseus' journey home. While there are many, many conflicts that happen throughout the story that covers 20 years, which is how long it took for Odysseus to get home after the Trojan War, the main conflict is Odysseus trying to get home. He is met with many obstacles and challenges that he must face and overcome, and there are conflicts within all of these, but the largest conflict is him trying to go home.
Some of the smaller conflicts or challenges that Odysseus faces throughout his journey are the monsters Scylla and Charybdis, the cyclops Polyphemus, and getting stuck on an island, as well as the wrath from multiple gods like Poseidon and Helios. When he does finally arrive home, he faces the large conflict of the suitors, who have taken over his house in his absence and have been trying to take his wife as well. Odysseus kills them all.
In spite of all the conflicts that Odysseus faces, he succeeds in arriving home to his wife and son after being gone for 20 years. He completes his odyssey.