This error means that a script is trying to run (usually the SQL install script for an extension) in a directory where scripts are not allowed to run as defined in your php.ini or Apache config file (depending on your configuration). This is a security feature within php designed to disallow untrusted scripts to run.

To resolve this you should either comment out the line or add in the directory where the script lies, on a standard install the line is commented out (see screen shot attached).

The full error will look something like this:

a:5:{i:0;s:509:"Error in file: "/var/www/vhosts/your-domain
/httpdocs/app/code/community/Webshopapps/Productmatrix/sql/

productmatrix_setup/mysql4-install-3.0.2.php" -

Warning: realpath() [<a href='function.realpath'>function.realpath</a>]: open_basedir restriction in effect.

File(your install path) is not within the allowed path(s): (/var/www/vhosts//httpdocs:/tmp)  in

/var/www/vhosts/httpdocs/app/code/community/Webshopapps/

Productmatrix/sql/productmatrix_setup/mysql4-install-3.0.2.php on line 2";

i:1;s:1060:"#0 /var/www/vhosts/httpdocs/app/code/core/Mage/Core/Model/Resource/Setup.php(374):

Mage::exception('Mage_Core', 'Error in file: ...')