This is a shield for the CC3000 WiFi Module. The CC3000 from TI (Texas Instruments) is a self-contained wireless network processor that makes incorporating internet connectivity into your project simple. Instead of the more standard UART communication method, the CC3000 module utilizes an SPI interface allowing you, the user, to control the flow of data as you please.
Your ESP8266 is an impressive, low cost WiFi module suitable for adding WiFi functionality to an existing microcontroller project via a UART serial connection. The module can even be reprogrammed to act as a standalone WiFi connected device--just add power!