Pimcore requires write access to the following directories:
If you know which user executes php on your system (PHP-FPM user, Apache user, ...), simply give write access to the appropriate user. Execute the following commands on the shell (eg. via SSH, …) - replace YOURUSER and YOURGROUP with your configuration:
chown -R YOURUSER:YOURGROUP website/var pimcore
On Debian systems (and most other Linux distributions) mostly the www-data user executes the php files, just execute the following commands in your install directory.
chown -R www-data:www-data website/var pimcore