the problem is you are trying to dump to a directory that very likely doesn't exist or you don't have access to. What you will need to do is dump to your filespace, then FTP on to your local machine.
This is the code you will need:
then to install it:
mysqldump --opt -uyour_username -pyour_password database_name > /path/to/dump/file.sql
and to find out the path to dump the file to (i.e. the top level of your host type cwd at the bash prompt.
mysql -uyour_username -pyour_password database_name < /path/to/dump/file.sql