CQ has two types of dialogs:
"dialog": The content entered with this dialog is stored directly to the paragraph on the current page.
"design_dialog": The content entered is stored to a "design page" created in /etc/designs.
In previous versions of CQ, back to CQ 4, the idea of the design dialog was to store content in a place other than the paragraph of the current page. Since in the early days this type of content was related mostly to design content (e.g. font size of a navigation, etc.) this page was called a "design page".
The design page is assigned to a content page via "page properties". In the page properties you can select a design page and every new child page you create will "inherit" that design page. If there is no custom design page, then the "default" design page will be used (/etc/designs/default). Note that you cannot do anything with the design page, it's simply a node to collect content provided via "design_dialog". So if you have content you want to share among the child pages, you can use a design dialog so store it to a design page.
Hope this helps.
