The ESP8266 is a combination of a microprocessor and WiFi. You can program it with the Arduino IDE and if you do not need very many I/O pins you would not need to use a regular Arduino board with it. The ESP8266 microprocessor is a lot faster and has a lot more memory than an Uno or Mega.You can buy the ESP8266 as a bare module in a few different configurations but it would probably be more convenient to buy something like the Wemos D1 board or a similar device.If you want more info have a look on the ESP8266 Forum.If you do want to use an ESP8266 in conjunction with an Arduino board then the usual arrangement is to establish a serial connection between them....R
But I would like to know if I connect the module to my Arduino UNO, will I be able to somehow set it up to act as a router access point for my mobile phone to control it? Or even better, if they could talk via a 3rd router?
I would like either the first module or wifi shield to act as a router for mobile devices.