First, the title: the Southern Cross, or Crux, is a large constellation visible in the night sky in the Southern hemisphere.
Stephen Stills wrote this song while taking a long boat ride in the South Pacific, in the aftermath of his divorce from French singer/songwriter Veronique Sanson. The marriage had been a very difficult one, and the divorce was no easier, as both parties fought in court for custody of their son.
During the long boat trip, Stills started to calm down and sort out his feelings. Seeing the stars at night from a boat in the middle of the ocean, he got a sense of how small and petty his own problems were, and how unimportant his quarrels with Sanson had been.
And he begins to realize that, before long, both he and Sanson will be all right, they'll both find happiness wiht new partners, that Stills will always draw his greatst strength and inspiration from music, and that eventually, he'll be able to look back and appreciate the GOOD things that came of his marriage.