According to the help section:
When checked, Picard will use the type of the first image retrieved as the filename when saving all images. If left unchecked, each file will be named according to its image type.
In practice, the opposite behavior is true. In other words, when the box is checked, the file type (front, booklet, etc) becomes the file name for all downloads. When unchecked, all files will be named the same according to the first image type.