In the first line of sketch #include <ESP8266WiFi.h> we are including ESP8266WiFi library. This library provides ESP8266 specific Wi-Fi routines we are calling to connect to network.

The first library ESP8266WiFi.h is required by default if we are using ESP8266's Wi-Fi. The second one WiFiUdp.h is needed specifically for programming of UDP routines. Once we have libraries in place ...