If there is no internet connection then things of course fail.
When you request a web page, the first thing that has to be done is convert the address like www.thinkbroadband.com
to a number (IP address), this process uses name servers. If there is no Internet this look up fails, hence the log entry made.
Sometimes it might only be the name servers that have gone down, but the rest of the Internet is alive, this often results in some things still working as your computer already knows the IP address from a previous lookup, but pages you haven't visited in a while show an error because the name can't be looked up. You can change your name servers if your ISPs servers are not very reliable. See https://whatismyipaddress.com/switch-dns