The name TiddlyWeb is based on TiddlyWiki. TiddlyWeb's original goal was to provide a flexible server-side for TiddlyWiki and get tiddlers on the web. The story at Why may be of interest.
The fundamental promise of TiddlyWeb is the storage and provision of individual tiddlers that can be accessed with their own URI. All other aspects of its structure fall out from providing a reasonable web service for the tiddlers.