From the MySQL Documentation on mysqldump
mysqldump requires at least the SELECT privilege for dumped tables, SHOW VIEW for dumped views, TRIGGER for dumped triggers, and LOCK TABLES if the --single-transaction option is not used. Certain options might require other privileges as noted in the option descriptions.
You said in your comment
There is a trigger but its not needed ( in the backup)
You either need the TRIGGER privilege or you can issue the mysqldump like this
mysqldump -h host -u backup -p database --skip-triggers | gzip > /tmp/test.gz
Give it a Try !!!