Great Rsiegel........ Thanks.....
As suggested, I have uploaded the code in my Arduino Uno Board connected with Wifi8266 Shield on RX at 7 and TX at 8 Pin.
/*Cayenne ESP8266 Shield WiFi Example
Adapted from Blynk's ESP8266_Shield_HardSer Example
This sketch connects to the Cayenne server using an ESP8266 WiFi module as a shield connected
via a hardware serial to an Arduino.
You should install the ESP8266HardwareSerial.zip library via the Arduino IDE (Sketch->Include Library->Add .ZIP Library)
from the Cayenne extras/libraries folder (e.g. My Documents\Arduino\libraries\Cayenne\extras\libraries) to compile this example.
NOTE: Ensure a stable serial connection to ESP8266!
Firmware version 1.0.0 (AT v0.22) or later is needed.
You can change ESP baud rate. Connect to AT console and call:
For Cayenne Dashboard widgets using digital or analog pins this sketch will automatically
send data on those pins to the Cayenne server. If the widgets use Virtual Channels, data
should be sent to those channels using virtualWrites. Examples for sending and receiving
Virtual Channel data are under the Basics folder.
//#define CAYENNE_DEBUG // Uncomment to show debug messages
// Cayenne authentication token. This should be obtained from the Cayenne Dashboard.
char token = "";
char ssid = "";
char password = "";
SoftwareSerial DebugSerial(7, 8); // RX, TX
#define CAYENNE_PRINT DebugSerial // Comment this out to disable prints and save space
// Set ESP8266 Serial object
#define EspSerial Serial
// Set ESP8266 baud rate
Cayenne.begin(token, wifi, ssid, password);
But now the issue is, I have removed the USB Cable from the computer, how I can check whether the Arduino Uno board is connected successfully to my router or not? Is my Arduino Uno board now working as a access point? or what? I can see some ESP_14C03 wifi connection OPEN in my available wifi connections. If this works as a access point now, then can I change the SSID and how can i secure this wifi connection?