The transclusion variable is set by the $transclude widget to a string that identifies the position of that widget within the widget tree.
TiddlyWiki's core uses it to detect recursive transclusion. It is also used to implement the qualify macro.
The string has the following syntax:
Many of the five items are often blank.
In the sidebar, the value of transclusion is:
{|$:/core/ui/PageTemplate/sidebar|||}
When the tiddler HelloThere is displayed in the story river, transclusion is set to:
{HelloThere|HelloThere|||}