It's called "The Question Settled" and the cat on the right represents the South - or to be exact "Jeff" as in Jefferson Davis, the white cat represents the North as indicated by "Old Abe" on his collar, and the cat on the left has a ribbon labelled "contraband" which is what the enslaved people, rescued from the Confederacy by the Union Army, were called.
This version from the Library Company is in better shape than the one in the Library of Congress, but you can still see spots and stains on the image. I'll have to clean that up with Photoshop one of these days. More about the image here.
