The corset cover is a 19^th Century washable undergarment that is worn over the corset to protect it from spills and rubbing from the bones of the bodice. The corset cover buttoned center front which distinguishes it from the camisole, which didn't button as the corset would have pushed the buttons into the skin. 

Quoted from Lei Hidic crinolinegirl on the VFG Forums "tell tale piping, dropped shoulder seams and the open work that 1860's and early 1870s corset covers tend to have... but what sets this apart from an 1860's one, is the long basque and peplum all around it. With 1870's bodices starting to grow longer into the cuirass bodice style, corset covers reflected this.

c.1910 Corset cover with Broderie Anglaise and ribbon insertion.
Courtesy of artizania