Atoms are an X11 concept. They map strings to an integer identifier allocated by the X server. In the context of Tk, each widget is assigned a pathname, which is stored as an atom. The atom has a string name (you can get it for each widget by using the PathName method) and a 32-bit ID. These methods are used internally to handle things such as the selection mechanism.
To get the 32-bit ID for a given widget, send the name of the widget to the atom method:
$id = $widget->atom($widget->PathName);
You can do the opposite and use the ID to get the name of the atom back. To do so, use the atomname method:
$name = $widget->atomname($id);