It's a 1985 anime featuring anthropomorphic cats taking a dreamlike, allegorical journey. It's got some Christian imagery, and it's very slow (in a way I like, but others might not). It reminds me a bit of Saint-Exupery's The Little Prince, and several other reviews of it I found on the web also made that comparison.
I don't think I liked it, but it was interesting, and what I really got out of it was this: It was a missing link that helped me understand why there is a subgenre of anime featuring anthropomorphic cats taking dreamlike, allegorical journeys. The other two examples of this I've seen (Cat Soup and Tamala 2010) are quite a lot different from Galactic Railroad, especially in that they are more gory/violent, but all three seem to partake of something similar. I also thought perhaps Haibane Renmei owed something to it - HR isn't about anthropomorphic cats or physical journeys, but it is about transitions. The book that Haibane Renmei took some elements from—Hard Boiled Wonderland and the End of the World—also fits in.
Maybe as I watch/read more I'll have a better understanding of the ways in which these works are primarily talking to each other and the ways in which they are representative of larger themes in Japanese culture/ art/ literature.
(The icon is from Cat Soup.)