A breakout board is used to connect a ribbon cable to a breadboard, allowing larger circuits to be prototyped more easily. The two rows of pins on the breakout board should go on either side of the central divide on the breadboard:
Breakout board clipped in place on a breadboard.
If you do not have a breakout board, it is possible to plug wires and components directly into the Pi’s GPIO pins.
Breakout boards can be purchased as part of Adafruit’s breakout kit.