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. After all, one purpose of creating VLAN is to help facilitate improved security in the network.
For a home network, this configuration is more than adequate to provide separate VLAN networks especially if you do not need to have a large amount of communication between the VLANs. The router on a stick configuration could actually become a bottleneck if you have high bandwidth requirements between VLANs since the network traffic must be sent to the router on a single ethernet interface in order to forward the data to the other VLANs on the same switch.
For example, if you are using a 1 gigabit switch and a router with 1 gigabit ports but are pushing more than 1 gigabit of data between your various network devices, you will encounter a bottleneck with this network configuration. A general recommendation is to make use of a Layer 3 switch that can route traffic between other switches without needing a router for inter-VLAN communication. Layer 3 switches can process data packets faster than routers since data is transferred at wire speed. Higher end switches often have high bandwidth ports (10 gigabit or higher) that may be used to connect to other switches to improvement performance as well.