Ok, this is what I did.
Like Brian Mc said, I checked my logs at /var/log/system.log. I found a little extra information. This is what the full line in the system log reads:
Mar 12 04:43:29 10242-MacBook-Air ddnsd: [03/12/2016 04:43:29] [Emergency] [update thread] uncaught exception: easyDNS Runtime Exception
So I was like, huh! What's this "ddnsd" thing? So I looked through my processes for any process with a name like ddns.
ps aux|grep ddns
The command came back with:
abudu_h 1142 0.0 0.2 2538864 6496 ?? S 7:24AM 0:01.27 /Users/abudu_h/Library/Application Support/easyDNS/ddnsa.app/Contents/MacOS/ddnsa
I thought, I don't really need this program running, why not turn it off. So rather than delete it, what I did was make it non-executable.
cd /Users/abudu_h/Library/Application\ Support/easyDNS/
chmod -x ddnsa.app/
And hooray! The messages stopped.