octoprint seems to have a setting that involves googles DNS server.
The program is pinging that address to check the internet connection to "prevent resource intensive operations if it's already clear that they won't succeed anyhow". It checks for connectivity, if it has it then it will check for update otherwise it won't check for an update.
That's just Google's DNS (name resolution) server. 220.127.116.11 and 18.104.22.168 are the Google values. Your ISP will also have a DNS server that you could use, which is what it says to use Google's "if you don't know what to set here".
Using the Google values are your best bet since they'll pretty much absolutely always be online and available.