What trip is literally and figuratively being referred to in "O Captain! My Captain!" by Walt Whitman?

Structurally speaking, "Oh Captain! My Captain!" is framed as an extended metaphor involving a ship being brought into a harbor after having traversed difficult conditions, with the Captain lying dead as it reaches a safe destination. This image of the ship sailing into the safe harbor is the literal reading of the poem.
However, symbolically, this poem is shaped by the experience of the Civil War and of Abraham Lincoln's assassination. The ship which has gone through those difficult conditions represents the United States, which has gone through the turmoil of the Civil War, while the Captain refers to President Lincoln, assassinated by John Wilkes Booth. Lincoln provided leadership, guiding the country through one of the most traumatic experiences in its history, only to be murdered at the end of it.