re: Simple home networking for beginner

The "controller" is just the software that configures and manages the network. For a basic home router, you don't really need a controller... you can set up and manage the network completely via its web UI. When you get into multiple devices, it becomes very handy to manage everything via one cohesive UI rather than configuring each device individually.

As mentioned above, you can manage TP-Link devices without a controller, but you can do the same with Ubiquiti. It's just a pain, and it's better to have a controller.

Ubiquiti has always offered standalone controller software which you can install on any machine (TP-Link offers the same), but more recently Ubiquiti has gone to more of a plug-and-play setup where the router/gateway runs the controller software. They call it UniFi Network, so any gateway that says it runs Network will serve as your controller. The Dream Machines, the Dream Router, UniFi Express, and Cloud Gateway Ultra all run Network.