I've watched it enough times (in both languages) to get the ending. Most of Shinkai's films need at least more than two viewings to really get them. (Hoshi no Koe took me 4 times.)

The tower was breaking the separation between two worlds, and was going to engulf and destroy the planet. Sayuri was keeping it shut, exactly how is never explained. They realized that they needed to bring her to "their promised place" to bring her back and out of her coma. Doing so would destroy the world, which is why she had never left on her own. The tower was the only place where they could reconnect, and thus the only place where she would ever come out of the coma. They had to get to the tower before it was destroyed, or Sayuri would be lost forever.

The last line is key. "In a world in which we lost our promised place, we've begun to live again." Happy endings all around.