They must be two sets of twins. The back of this CDV doesn’t tell us anything about them, but it does identify the photographer, C. W. Gill.
I didn’t find anything about Gill online. The Hubbard Block was built on Public Square by Volney Stow Hubbard in 1868, which is about when this photo was taken, I’d guess. Other photographers had studios in the Hubbard Block at various times, but Gill’s must have been one of the first.
The studio is completely bare, without a backdrop or rug, which may be an indication that Gill hadn’t been in the building very long. I find the checkerboard floor very appealing, and the plain wall allows our gaze to remain on the sitters. The women in back are holding hands, and each has placed her other hand on the shoulder of the sitter in front of her, suggesting a degree of familiarity.
Did these four young people decide to have their picture taken together, or did someone else suggest it? A hint of a smile tells us that at least one of the four was enjoying herself.