Visibility in an Active Structure context refers to the ability for any point in the structure to be able to find and connect to any other point in the structure. The variables throughout the structure expose the messages in the structure and also support the semantics of the structure - each variable has a name in a multi-parent hierarchy.
Visibility also implies that activity needs to be 'atomic' - irreducibly small in size, before the results of the activity become visible and actionable.
Contrast this visibility with variables on a stack - the variables are not accessible, except through the stack frame pointer, and only the program connects them.