Sure, no problem. For a simple example, consider a basic book with named chapters. You probably would assign the title with a particular paragraph style, which perhaps you have named "ch_title." Next, you can assign a variable that is linked to ch_title. In InDesign, there are a couple of choices, such as "First use on a page," which will grab the text from the first time that paragraph style is used in a page. Next, you can then create your header on a master page, and in the header, you place your variable. Now you have running headers, so that on the top of every page, you have the name of the current chapter. The value of the variable will stay the same until the next time it comes across the same paragraph style. If you have to edit the text of the chapter title, the running header will pick it up.
You can also think of it in terms of a similar but more limited functionality within Publisher as it is now. To use the same scenario above, you could instead divided your pages into sections in the Pages Studio and name each section to match the corresponding chapter title. Then you can use the <section_name> field in the header, and it will work basically the same. There are two disadvantages with that for a simple book: 1) You must make the section name match the chapter title, and make sure if you edit the chapter title, you also edit the section name, and 2) If the page count or order gets changed, you must make sure the sections still line up with the chapter. However, with a little vigilance, it is not a bad solution for Publisher's first version.
To give you an example that is too complex for Publisher, here are three pages from a layout of the French Bible that I have been working on lately in InDesign.
If you look at the top left of page 322 and the top right at 323, you will see running headers that show the first and last full verses on the spread. That is a combination of a couple of variables: first, it is defined from a character style on the book heading "2 Samuel," and secondly, each verse has a hidden verse reference (for example 1.22) that is tagged with the character style chap-verse-hidden. Then on the left page there is a variable defined to the first use of chap-verse-hidden on the page, and on the right we have another variable that is defined as the last use of chap-verse-hidden on the page. In that way, we have a faithful set of running headers throughout the text.
Similar would be a dictionary, where in the headers you have the first and last entry. If each entry is styled with a character style, then variables makes it simple to make running headers such that no matter the text flow, the first and last entry in a spread is automatically put in the headers.
Wish: support for Text Variables. Very handy e.g. to define revision numbers and other stuff and inject document metadata (date printed, modified, created, etc.) at appropriate places. Makes the document more evolvable (maintainable).
Wish++: share Tet Variables across documents (Designer, Publisher, Photo).
I didn't knew that, thanks for the clarification. I was just repeating what the warning that prompt when opening one of those files, currently is still true... in semantics... because I can open them and save them as Publisher files and I still be able to reopen the original file on the original App.