What are Icon\r files and how do I delete them?

The Icon\r file is used when you're about to change folder's icon: when you change the icon, it is not actually applied to the folder itself but rather to the Icon\r file inside the folder in question.

You can remove the file via terminal with rm $'Icon\r'

Alternatively, if you want to delete the file through Finder, you must make it visible first; also something you can do via terminal: SetFile -a v $'Icon\r'

Somewhat related info on how to change file's or folder's icon via Terminal: Changing a file or folder icon using the Terminal

… And be sure to see Icon? file on OS X desktop on Super User.