Normally the config for a virtual network called "default" is installed as part of the libvirt package, and it is setup to autostart when libvirtd is started.
If, for some reason, the "default" network (or any other locally-created network) could not be started, any domains configured to use that network for its connectivity will also fail to start, giving the message in the title.
One of the most common causes for a libvirt virtual network's failure to start is that the dnsmasq instance required to serve DHCP and DNS requests from clients on that network failed to start. To determine if this was the cause, run the following command from a root shell:
virsh net-start default
If it is successful, the problem was some other intermittent condition that has now passed. If not, look in /var/log/libvirt/libvirtd.log for the full error log message. If you see a message similar to the following:
Could not start virtual network 'default': internal error Child process (/usr/sbin/dnsmasq --strict-order --bind-interfaces --pid-file=/var/run/libvirt/network/default.pid --conf-file= --except-interface lo --listen-address 192.168.122.1 --dhcp-range 192.168.122.2,192.168.122.254 --dhcp-leasefile=/var/lib/libvirt/dnsmasq/default.leases --dhcp-lease-max=253 --dhcp-no-override) status unexpected: exit status 2
(the important parts are "dnsmasq" and "exit status 2") then the problem is most likely a systemwide dnsmasq instance that is already listening on libvirt's bridge (thus preventing libvirt's own dnsmasq instance from doing so).
1) If you're not actually using dnsmasq on this machine to serve DHCP for the *physical network*, you should just disable dnsmasq completely.
Here is a handy pointer to instructions on starting/stopping/enabling/disabling systems services on various flavors of Linux:
http://linuxhelp.blogspot.com/2006/04/enabling-and-disabling-services-during_01.html
2) In the unlikely case that you do need to run dnsmasq to serve DHCP for the physical network, you should edit /etc/dnsmasq.conf, and add (or uncomment) the following lines:
bind-interfaces interface=[some physical interface name, e.g. eth0] listen-address=[ip address of the interface you want, e.g. 192.168.1.1]
(pick one of either line 2 or line 3, but not both)
After you've made this change and saved the file, restart the systemwide dnsmasq service (see the above link for directions specific to your Linux distro).
Now you should be able to start the default network:
virsh net-start default
and after this, you should be able to start your domains.