You just found out that the SMTP server that your SharePoint server needs to configure in the Outgoing E-Mail Settings does not listen on port 25.
The bad news is that SharePoint does not allow you to configure this. It always connects to port 25 because only the foolhardy would use an alternate port.
The good news is the steps to get around this using the SMTP service installed on to the SharePoint server have been documented by David Lozzi at Sending SharePoint emails through alternate ports
If you are using Exchange Online as your SMTP server to send emails you can follow the instructions at Step by step configuration of Outgoing Emails from SharePoint to Microsoft Online
If you have configured your outgoing email settings but are having issues sending emails from SharePoint verify that your SMTP server is allowing connections from your SharePoint server using Telnet.
If your SharePoint server does not have the Telnet Client installed you can install this from the Server Manager > Add Roles and Features wizard in Windows Server 2012. The Telnet Client is in the features list.
Eric Lough has a detailed article Troubleshooting SharePoint SMTP Errors via Telnet which describes the telnet commands to use.
If the issue turns out to be Exchange Server not allowing your SharePoint server to relay emails and you can’t find the Exchange server guru in your organization or you are the Exchange Server “guru” in your organization follow George Khalil’s instructions at Configuring outgoing email in SharePoint 2010 with Exchange 2010 – Step by Step Guide to get you out of that mess.