In CIAO, a stack is an ASCII file containing a list of filenames. Many CIAO tools can accept a stack as an input in place of a single file via the @ qualifier. The tool runs on each file in the stack consecutively; some tools create a stack of output files, while others combine the results into a single output. For details, see the stack ahelp file.
The term "stack" is used similarly when referring to region shapes in a file. The Regions with Multiple Shapes vs. Region Stacks section of the Using CIAO Region Files explains this and gives an example.