The war being referred to here is the Trojan War, in which an army of united Greeks sailed to Troy to retrieve Menelaus' wife Helen, whom the Trojan prince Paris had taken. The war lasted ten years, fought outside the city walls. Homer’s earlier epic, The Iliad, dealt with events surrounding the anger of the hero Achilles during this war. The story of Troy has been a favourite subject matter of writers and artists ever since.
We meet both Helen and Menelaus in Book 4 of The Odyssey, when we will hear a little more about Helen's role in the war.
At this stage of the poem, it has been ten years since the Greek survivors from Troy reached their homes, but there is still no sign of Odysseus. His wife, Penelope, has now been parted from her husband for twenty years since he set sail to fight at Troy.