authentication and configure SMTP settings

[CTGO.co]

 I just got this message from my hosting company:

Dear Customer,

You should use SMTP authentication. You will configure SMTP settings and sending emails.

what is that means ??  Is there something wrong or missing in the settings which we edited ??  check please the screenshot and tell me.

Thank you

[CTGO.co]

I try to verify new clients subscription to website but the website's email doesn't sent emails to subscribers. what is solution??