The ESP8266 is a little computer gizmo with bundled WiFi that's easy to incorporate into a wireless control system. The on-board computer is tiny, but it's powerful enough to run a MQTT client. MQTT in turn is an extremely light-weight message-oriented communication system. The example shows an ESP8266 with custom software controlling a relay, that in turn controls enough AC power to turn a light on/off. Controlling the relay is fairly simple, since the ESP8266 has an output strong enough to drive the coil of a relay.