A Stacked transition stores/pushes the state (the one that just got finished) into a stack. Once the FSM encounters a finished state that has no outgoing transitions (thus nowhere else to go), an automatic transition takes place to the previously stored/stacked state (with no need for direct transition connections).
If multiple Stacked transitions are made (thus multiple states are in the stack), then the order of such automatic transitions mentioned above, are done from the last state stacked back to the first (last in, first out).
A “Clean” transition simply clears the stack (I should mention that in the help text). Other than that it is a normal transition.
One of the demos in the downloadable example scenes is actually utilizing a Stacked transition as an example you might want to check out as well.