A traditional file system, such as FAT or NTFS, has its contents organized in a hierarchal directory structure and is relatively slow in searching the content by particular attributes.
If you organize your pictures in folders "by Dates" — there would be no way to access them "by Persons", "by Events" etc… You are to use third party custom software like Adobe PhotoAlbum® to perform this task.
WinFS overcomes the hierarchy and "flattens" the storage of individual files (i.e. there is no "hierarchy" based on directory and file names), and it enables searching for items by their attributes (like date the photograph was taken, who or what is in the picture, what camera was used to take the picture, etc).
WinFS also extends this idea beyond the kinds of information that have been traditionally stored as files on a file system. WinFS can understand any arbitrary set of data, such as a "Photo" or an "Email" or a "Calendar".
Applications today must store these kinds of information in their own custom database; if other applications want to gain access to this information, it's quite a lot of work because there is no application-neutral storage mechanism for this kind of information.