The Trojan war is a war between the Greeks and the people of Troy. The war started when Trojan prince, Paris, abducted Helen, wife of Menelaus of Sparta and refused to release her. As of so, he had asked his brother to to lead an army against Troy.
In order to defeat the Trojans, the Greeks built a hollow wooden horse and gifted it to the Trojans. When they had brought the horse into the walls of the city, Greek soldiers climbed out of it. That brought the defeats of the Trojans.
I feel that the Odyssey is related to the Trojan war because the war gave a start to the story of Odysseus. The story of Odysseus began when the war ended and he and his men were voyaging home back to Greece (I think).