This is how Kennel Connection processes emails:
When you hit Send or it's time to send automatic emails, KC logs into your email provider's server. Once the login information has been authenticated, KC sends all emails to your provider. That's all it does. Your provider will then send the emails to your clients.
This error means the email server KC is trying to access does not allow this type of connection. It usually is because of the Port setting in File, Business Info, Email tab. For example, Port 25 is not a secure port. You can try 465 or 587 and check "Use TLS". If that doesn't work, you'll need to contact your email provider to find out what port they want you to use.