As I have mentioned, routing is the act of sending source packets to a different destination; they could go across a WAN or a different VLAN, but some sort of routing must take place, by using a router. If you do not have multiple VLANs or must go across the internet to reach a branch office, well, then there is no routing needed. If that's the case, you must be on a small network or a bogged-down network.
Think about the scenario in the following screenshot:
The preceding screenshot shows a very common configuration used by schools: they have switches in their classrooms, all in the native VLAN, connected to a core switch, which then gets connected to a router. At this point we are all still on the same network, but with different IP addresses; however, once it goes to the public side of the router, we use a public IP address so we can access the internet...