First you need to know a bit about how name resolving works in Ubuntu since Ubuntu 12.04.
Stéphane Graber blogged some information about it last year (https://www.stgraber.org/2012/02/24/dns-in-ubuntu-12-04/). The most important thing to know is that both Ubuntu Server and Ubuntu Desktop use resolvconf to manage the resolv.conf file. That means that you should no longer edit /etc/resolv.conf directly; instead you should configure your network interface configuration utility to provide the right information to resolvconf. For Ubuntu Server the network interface configuration utility is ifup and it is configured by the file /etc/network/interfaces. For Ubuntu Desktop the network interface configuration utility is NetworkManager. This is what you are using.
NetworkManager is configured by means of network indicator |
Edit Connections.... However, for network interfaces configured by DHCP it normally isn't necessary to change any settings manually. Normally what happens is that the (remote) DHCP server provides to NetworkManager both an IP address for the local interface and the address of a (remote) DNS nameserver to use. NetworkManager starts an instance of a forwarding nameserver that listens locally at 127.0.1.1. This address, 127.0.1.1, is sent to resolvconf which puts
nameserver 127.0.1.1 in /etc/resolv.conf. NetworkManager also gives the (remote) IP address of the DHCP-provided DNS nameserver to the forwarding nameserver. Thus a program running on the local system asks the resolver to translate a host name into an IP address; the resolver queries the local forwarding nameserver at 127.0.1.1; the forwarding nameserver queries the remote nameserver(s) it has been told about, receives an answer and sends it back up the chain.
NetworkManager communicates with the forwarding nameserver process over D-Bus. You can see what NetworkManager told the forwarding nameserver by running the command
nmcli dev list iface eth0 | grep IP4.DNS.
Update arising from the comments: Note that resolvconf actually writes the file /run/resolvconf/resolv.conf to which /etc/resolv.conf is supposed to be a symbolic link. If /etc/resolv.conf is not a symbolic link then you need to recreate it. To do so you can run
sudo dpkg-reconfigure resolvconf or
sudo ln -sf ../run/resolvconf/resolv.conf /etc/resolv.conf.