Help choosing a suitable device

I need a device to be able to connect to a electronic board (wired, wireless), and the connection to the device must be wireless using Wi-Fi not Bluetooth, is there any similar device matching my requirements ?, i am developing a mobile app, the app is connected to the Wi-Fi and will be sending commands WIRELESSLY to the device, and the device the receives the command and give the electronic PCB board which i have developed a certain command, the communication between the device and the pcb can be either wired or wireless,

I hope I made myself clear enough,
Can anyone please help pick a suitable device ?,

Thank you in advance,
Alexy Ibrahim

The Arduino Yun has Wifi built in

Or there are various Arduino Wifi Sheilds http://arduino.cc/en/Main/ArduinoWiFiShield

Or various other external Wifi devices that you could use.

The Arduino has multiple IO pins than can drive small loads (40mA) or control larger loads via suitable hardware

The XBee S6B might be all you need.