The ESP8266 is a simple standalone addon for any board that works fine with Arduino and only cost less than 4€ on ebay.
It can operate as a device or an AP can gives wireless network connectivity to your application. It is interfaced with Arduino based on a serial line. The only problem of a such thing ( as for most of wifi chip ) is the power consumption. It requires about 150mA to run ; a lot for batteries.
My Friend @couac made a really good post on how to make it working with a Yabas, basically any Arduino board, I recommand the reading of his post : william post on ESP8266