I think it's most likely just a utility variable that you can use to reference an object. Stack object seems to always be implicitly set to the callee on queuing an interaction, though it can be changed to another object or null without altering the execution flow.
I'm still not sure of its relation to stack frames. It seems that the stack object carries onto any subroutines, but any changes to it remain in that subroutines stack frame (would explain the naming, "stack object".) In the module inspector, it's roped in with the parameters and locals.