To send e-mail via an SMTP server from your PC, you will need a mail client (or mail program). Mail clients include Microsoft's Outlook and Outlook Express. The mail client communicates with a SMTP to copy the mail from your PC to the SMTP server. The SMTP server then communicates with the recipients mail server and delivers your mail to the recipients mailbox.

Although SMTP doesn't have an authentication system per se (because it is Simple), illicit spamming from normally open SMTP servers became a major nuisance some time ago, so caused the industry to come up with an authentication mechanism that would prevent illegal use

The authentication mechanism in general use is called POP-Before-Relay.
Which in practice, means that to use SMTP you must have a POP3 email account on the same server which you are using to SMTP email from.

When you 'POP' your mailbox and collect email, simultaneously it registers your IP address in a special 'allowed' table, and a relay window is opened for your current IP address, and you can send email via the SMTP server. The window is opened for 15 minutes or so, then it closes. POPing the mailbox re-opens it again.

For this to work successfully, make sure that 'My server requires authentication' is checked on the 'Servers' tab in your account settings.

The mechanism is reasonably stable and reliable working without a problem in 99% of cases, however there are occasions when people are connecting from proxy IP addresses, or behind some firewalls and will get denied relaying of their email.. An error message saying Relaying denied is shown in the mail client's error dialog box is the usual result.

Generally speaking, this happens mostly on business or corporate networks, and occasionally when connecting remotely through a hotel or other wireless point, particularly when abroad. There is nothing that you can do to bypass these issues apart from try connecting from another location.

Where the issue is on a corporate network, you will need to get the company network engineers to reconfigure the network to enable access to port 25 on remote servers.

If you are getting a problem on your local PC, then the problem might be firewall related, if it isn't something simple like a miss spelling of mailserver name or username/password (or not having 'My server requires authentication' checked and enabled). 
Don't overlook checking the obvious causes before you go off tinkering with your computer's settings!!

You might try checking to see if port 25 is blocked by doing the following

Click on the Start menu button, usually located at the lower left corner of the screen. There is a tab called "Run". Click it and a new window will pop up. In the text field of this window you need to type cmd and then press the "Enter" key. Another window will open. It is the so called "MS-DOS prompt" or "command prompt". Just type the following command in the command prompt window and press "Enter":

telnet my-domain-name.com 25

Each Mac OS is delivered with a preinstalled terminal emulator. The terminal is a tool which allows you to execute commands from the command line. Usually, the terminal is located under your Mac HD -> "Applications" directory -> Utilities sub-directory. When the window opens, you will see a command line with a flashing cursor on it so you can start typing right away. Just type the following command and press "Enter":

telnet my-domain-name.com 25

220 my-domain-name.com ESMTP