The Trojan War was the catalyst that set The Odyssey into motion since it pulled Odysseus away from his kingdom of Ithaka, and beloved Penelope, and into the ten year struggle to win Queen Helen back for Greece.

Odysseus fights the Trojans (who have kidnapped Helen) alongside his fellow Aechans (Greeks) for ten long years until finally, with some inspiration from the gods, he spearheads the idea for the Trojan horse - a giant wooden horse disguised as a gift for the Trojans that hid the Greeks until nightfall and allowed them to attack the unaware Trojans from within their own city walls.

After the war ends (and this is what Homer's The Illiad is concerned with), the trouble really begins for Odysseus, as we know. So, the war not only causes Odysseus to be away from home in the first place but also is the impetus for all his other troubles, as he never properly thanked the gods for helping him to victory in the war, and we know how touchy those gods can be. In Odysseus's case, they heap an additional ten years of suffering and homesickness upon him, as though the war weren't long enough.

Good question. Broadly speaking, there are three or four general reasons the war is important in the Odyssey. Start with the basic one: Odysseus left home to go fight in it; that's why he was gone.

Next, events that occur in the war (gods offended) are why he is blown off course and delayed for so long. Taken together, you could say that the Trojan War causes the Odyssey.

After that, Odysseus's reputation is made by his heroics in the war; these show up when someone retells the story in his travels.

Finally, he sees his companions from the war in the underworld, so this poem gives us a chance to reflect on the meaning of the war.