Some translations are easier if we keep in mind the subject under discussion. In this case, the phrase appears in the politics section. I got zapped on the minister earlier because (as usual) my mind was in a fog and el clero was the first thing that it brought up. Apparition in Spanish would be aparición, and ghost could be a number of things such as fantasma or espíritu. If you look up manifestación on Google or anywhere online, I could not find an instance where it was used in the sense of a ghost or apparition, though in English we hear it that way a lot.
It's a partial cognate. Something is manifest if it's evident, or obvious or can be demonstrated. So a Manifestation is a demonstration, just that in this case a political protest is not the same type of "demonstration" that we think of for the English "manifestation".