An obvious application of a virtual network of VMs is for experimentation. Together with the -snapshot option of QEMU (and kvm), one can experiment with computer security and privacy practices (both offense and defense) without much worry. Of course, in this case, it’d be wise not to use a TAP device to connect to the virtual switch!
This is also a good learning tool to learn networking concepts such as DNS, DHCP and etc. Adding a DNS or DHCP server into a real network will typically cause massive confusion. However, with a virtual network of servers and clients, there is no danger of affecting computers in a real network.