It is a grave marker patterned after the
Southern Cross of Honor. The award was originally created during the war to be a counterpart to the U.S. Medal of Honor. Very few of those were given out during the war.
The award was reactiviated in the 1890s by the United Daughters of the Confederacy, to be awarded to any former Confederate who provided "loyal, honorable service to the South."
The men at center and right in this picture are each wearing one of those postwar medals.
The photo you've attached is a similar designation, a cast-iron cross placed on Confederate veteran's graves by SCV camps or by family members. These can be obtained through the SCV or other heritage organization. The example you provide is an altered photo
of this example in a cemetery at Natchez, Mississippi: