Character Analysis
We don't see much of Arwen in The Two Towers, but with this whole forbidden love-thing developing between her and Aragorn, they needed to fit her in the movie somehow. Originally, she was scripted to show up at Helm's Deep, but when that didn't work out they went for the classic dreamy flashback.
Arwen appears to wake Aragorn with some elf powers that we don't exactly understand. How can she speak to him half a world away? Does the power of love to transcend space and time? Whatever it is, we see Aragorn and Arwen speaking to each other of their love, but their hopes are cut short by Elrond urging Aragorn to let his daughter go, for her sake.
While Aragorn seems willing to make this sacrifice for the good of his love, Arwen will not give him up, she still has hope. Hope is a huge theme of the movie, and Arwen's hope is in the success for triumph in the war against the enemy. But that's not the worst of it.
Even if the war is won, Aragorn will still die a mortal man as Arwen lives forever with her grief. Maybe Elrond's never heard of "better to have love and lost than never to have loved at all." But, in the end, Arwen is obedient to her father, whom she loves, and travels away from Aragorn, into the west.