ESP8266 is really cheap (~$4) WiFi transceiver module that comes in many PCB configurations. WiFi module can be connected to other devices that can access and control it with AT commands, but fun part is that WiFi module can be used as stand alone device which can be programmed with LUA script which could perform simple tasks like connect to WiFi, control GPIOs and toggle LEDs or drive other devices.
Rui Santos have written a nice tutorial where he teaches how to set up a schematic of two LEDs connected to ESP8266 module. Then he demonstrates how to write a simple LUA script using ESPlorer Java based GUI and how to flash device with NodeMCU flasher. His example script enables WiFI module to work as web server where you can access it through web page and turn ON/OFF two LEDs by simply pressing buttons.