Celoxis requires an email account just like a regular person. The easiest way to debug is to setup a temporary email account in a program like Outlook, Thunderbird, Gmail, etc. with the same settings entered in Celoxis. If that works, then Celoxis should work.
Network: DNS or Firewall
If the email works from a program but not from Celoxis using the same settings in Celoxis, then it is either the machine on which Celoxis is running cannot resolve the hostnames you specified or firewall is blocking access.
If your email servers are using self-signed certificates, then it will not work. To check if that is the issue, please read this chapter.
For incoming emails to be properly acted upon by Celoxis, the Plussed Addressing setting should be correctly set. Please refer to this chapter for more information.