Hi Tony30
php.ini is the configuration file for your PHP installation, it could be located on different places ( phpinfo(); should return the exact location).
One of the parameter is execution_time=XX where XX is the time in second one script (php) could be running. Usually an script takes only a few ms or seconds to be executed, but on certain actions (as upgrading for example) it needs to take more time.
The problem here is that the upgrade script need to download the package, unzip it, copy the files, remove old files, perform additional actions (upgrading DB). All that actions take a while (updating the database from 2.x to 2.3 could take a long time because of some changes introduced).
You need to modify (or ask your hosting provider to) your php.ini file an increase that time. If that is not possible for you, then update manually