The find command works by traversing each directory from left to right starting at the point of the directory you provide. In your case, you directed find to start with the root directory which means it will end up traversing the entire directory structure of your file system.
In order to view the contents of a directory it is necessary to have read permissions for that directory. You, as a regular user, do not have read permissions for all the folders in your file system. Running the find command as a regular user, while find is traversing its way through the directory tree, every time it comes upon a directory where you don't have read permissions it will throw off a Permission Denied error message like you're seeing in the example above.
Instead run your command as:
sudo find / -name valgrind -type d
....and you will not run into all the Permission Denied error messages and find will be able to search through your entire file system for any directories containing valgrind.