permissions denied with perl/cgi script

My /usr/lib/cgi-bin/script.cgi must create a directory in my /home/myname directory, but in firefox appears:
Software error:

Cannot mkdir: Permission denied at /usr/lib/cgi-bin/script.cgi line 17.

For help, please send mail to the webmaster (webmaster@localhost), giving this error message and the time and date of the error.

I have the same problem also when I want make a folder in /var/www directory

What is the problem?

The script is being run by the web server user account which doesn't have proper access writes to create the directory.

I want to give to www-data user (apache2 user) permissions for make directory in specific directory.
How can solve this problem?