When adding an email account, you will be asked to specify an Outgoing Mail Server or SMTP Server. This is the mail server through which you will send email — which doesn't necessarily need to be the same as the mail server through which you receive email.
Ideally, your Outgoing Mail Server should be set to the same as your Incoming Mail Server, which means you will send and receive email through your web hosting account.
However, some Internet Service Providers will not allow you to send email through a different provider, such as your web hosting company. If you receive an error while sending a test email, here are two options:
Option 1: Enable SMTP Authentication and set an alternative SMTP port
In the same place that you specified the Outgoing Mail Server, you may find a way to set the port number of the Outgoing Mail Server / SMTP Server. In Microsoft Outlook 2007, for example, you would go to Tools > Account Settings > click the account and click Change > More Settings > Advanced, then look for the setting under "Server Port Numbers" labelled "Outgoing server (SMTP)".
Try changing the port number to 26 (instead of the default of 25.)
Then, under the "Outgoing Server" tab, check the box labelled "My outgoing server (SMTP) requires authentication", then "Use the same settings as my incoming mail server". This reduces the chance of emails you send being flagged as possible spam.
Option 2: Use your Internet Service Provider's mail server
If the above option does not work, change the port number back to 25, untick SMTP authentication, and instead change the Outgoing Mail Server to the one supplied by your Internet Service Provider.
Some common ones are listed below, but you should check with your Internet Service Provider if you are unable to send email with the suggested server listed below.
Telstra / Bigpond: mail.bigpond.com Internode: mail.internode.on.net Optusnet: mail.optusnet.com.au TPG: mail.tpg.com.au