The ending was open, we didn't get to see who the male character ended up with, but the final train scene was where he realised that that the person he once loved has moved one, but he couldn't.
Akari didn't looked back at him coz she was engaged, and that was a fragrant of memories which she let go off, but for Takaki it was everything.
The main theme song was written as a tribute to his gf who died of earthquake by the singer, it was a classical one.