>I went to my Outlook account setting and unchecked the box "This server requires an encrypted connection (SSL)" and now when I open Outlook I don't see the message about the Internet Certificate. Now I am wondering if I am better off with this box checked and the message or without. In my previous Outlook (Outlook 2010) I didn't have the SSL box checked and didn't seem to have any problems.

You may verify with your email host provider to see if this is required.