The Black Spires exist on the planet Batuu, a place nobody has really seen in the Star Wars universe yet because it’s the world that will be the home of Star Wars Galaxy’s Edge, the new land set to open at Disneyland and Walt Disney World in 2019.
The Black Spires themselves have been referenced as part of the promotion of the land done via a set of collectible cards, and they’re visible in the image above which was released along with the most recent announcement regarding when the new lands will open..
They’re geographic landmarks on the planet that lend their name to other locations, like Black Spire Station, but beyond that, we’ll have to wait and see what else, if anything, they may mean.