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Your system configuration does not currently support this feature. The handbook page on Clean URLs has additional troubleshooting information.
The problem can be solved by editing the .htaccess file: Just uncomment the line "# RewriteBase /" by removing the leading "#", save the file and reload the "Clean URLs" page in the administration interface. Now you should be able to enable the "Clean URLs" feature.
If you now have the problem that some images are not shown you will have to use the absolute paths of the images e.g. "/myfolder/image1.png" instead of "myfolder/image1.png".