The ESP8266 is a low-cost Wi-Fi chip/microcontroller, usually sold on a small breakout, which can be connected directly to the Pi and programmed in C, Arduino C++, or lua.
Expressif, who created the ESP8266, have a product page for the chip. They make a complete breakout as well. See also wikipedia and esp8266.net.
However, there are many different breakouts available from various manufacturers. Not all of them provide access to all pins/buses on the 8266, and the amount of flash memory varies (usually from 1-4 MB).
Since the ESP8266 uses 3.3V logic, it can be used directly with a Raspberry Pi.