A “router on a stick” (aka “one-armed router”) is a network configuration in which a single network switch is connected to a single LAN interface on a router. The network switch may be configured to have two or more VLANs to logically partition the network. The router is responsible for inter-VLAN routing so that network traffic may flow from one VLAN to another. This traffic is usually controlled via firewall rules to restrict certain traffic.
Setting up the Pi-hole DNS service is relatively straightforward on your home network. When you have VLANs configured, the setup is slightly more complicated. The issue is that you need to ensure that all of your VLANs have access to the Pi-hole server which is located on a different network (ideally, it should probably be located in your management VLAN to protect it from being accessed by your other network devices).