Okay so I have a wordpress site.
for example wordpress.com
On it I have a page called sports, I took some of these pages and put them under the page ‘summer’
So the url is now http://www.wordpress.com/summer/sports
However all the images are in wordpress.com So all the pages under the page summer, can’t see those images and all you have are image frames.
If you create the directory summer and put images in it, It will make it so when you go to http://www.wordpress.com/summer/sports, you will be taken to a blank page with only a single image.
So making a directory under the page name actually messes with wordpress and makes that page unreachable.
I presume you have used a relative path to the images on your pages, so when you moved them they no longer know where the image is in relation to the relative path. Using an absolute path would solve this issue (e.g. http://wordpress.com/myimages/test.png) you can then move your pages anywhere and they will always pick up the image or you need to change the relative path.
See here for explanation of relative & absolute paths: http://webdesign.about.com/od/beginningtutorials/a/aa040502a.htm