Breadboard is the piece of plastic component on top of your Education Shield. You may get a separate one in some examples. It looks (remotely) like a piece of bread, and is used for easily making circuits.
As you can see from the illustration, every line of holes are connected together. You can use this characteristic to connect different components, by plugging them into different lines on the breadboard, and the pins that should be connected together to the same line. You can also use jumper wires to connect two lines together.
Never plug the pins of a component to the same line, or it will not work.