Default route
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A default route, also known as the gateway of last resort, is the network route used by a router when no other known route exists for a given IP packet's destination address. All the packets for destinations not known by the router's routing table are sent to the default route. This route generally leads to another router, which treats the packet the same way: If the route is known, the packet will get forwarded to the known route. If not, the packet is forwarded to the default-route of that router which generally leads to another router. And so on. Each router traversal adds a one-hop distance to the route.
Once the router with a known route to a host destination is reached, the router determines which route is valid by finding the "most specific match". The network with the longest subnet mask that matches the destination IP address wins.
The default route in IPv4 (in CIDR notation) is 0.0.0.0/0, often called the quad-zero route. Since the subnet mask given is /0, it effectively specifies no network, and is the "shortest" match possible. A route lookup that doesn't match anything will naturally fall back onto this route. Similarly, in IPv6 the default address is given by ::/0.
Routers in an organization generally point the default route towards the router that has a connection to a network service provider. This way, packets with destinations outside the organization's local area network (LAN)—typically to the Internet, WAN, or VPN—will be forwarded by the router with the connection to that provider.
Host devices in an organization generally refer to the default route as a default gateway which can be, and usually is, a filtration device such as a firewall or Proxy server.