The format ePub3 Fixed Layout is ideal when you need to create an "exact replica" of the layout you created for your book originating, for instance, from a PDF or a JPG file.
Why couldn't you just publish a PDF then?
Because PDF is a format made for print, preventing a good visualisation on digital reading devices and, most of all, because it won't be accepted for publication in most major stores.
While the EPub3FXL is not only built specifically for digital reading but also is accepted in all major stores.
How to read a FXL?
Being a Fixed Layout format, the recommended reading devices to read them are smartphones, tablets and computers.
Most eReader don't support ePub3 Fixed Layout because of the technology they use, built specifically for text (with some exceptions like the Kobo Aura).
The ePub3 reads like a printed book, only in digital. It can be read in double pages or one single page.
You can read an EPub3FXL file using the Apple iBooks app, which is automatically installed on all devices.
2) Kindle Fire:
You can read a KF8 document (the equivalent of Mobi FXL) with the native reading app provided by Amazon.
3) Android Tablet:
You can read an EPub3FXL document using the Gitden Reader app, available from the Google Play Store.
You can read an EPub3FXL document with Calibre or Readium.
You can read an EPub3FXL document using the Apple iBooks reading app.