Session save path
From Joomla! Documentation
When installing Joomla! or visting Global Configuration (some extensions may also display this information) you may see a warning about Session save path being unwriteable. This means that the directory used to save information relating to a logged-in user's session cannot be written into - preventing the necessary data from being stored.
Generally this means that the user running the webserver's process (often a user called Apache) is unable to store files in the directory. This error should not be caused by this issue in later versions of Joomla! as sessions are saved to a folder within the Joomla directory structure.
Find the file php.ini, this is located in the same director as the installation of PHP
Open the file in a text editor and find session.savepath, this will look like :
We need to make this directory writable C:\DOCUME~1\username\LOCALS~1\Temp\php\session. for the user.
On Linux Systems the php.ini will probably use /var/lib/php/session folder.
How you update the permissions on this folder is entirely dependant on the setup of your server. If you use SuExec (so processes are run by different users) the easiest way is to ensure that all relevant users are in a user group and then assign the group permissions
chgrp /var/lib/php/session chmod g+w /lib/php/session
If it's only ever the apache user that runs your serving processes, you can simply change the permissions to ensure that the folder is owned by the apache user
chown apache /var/lib/php/session