The projects in this series of lessons all use something called Breadboard, or more accurately, Solderless Breadboard.
Breadboard is a way of constructing electronics without having to use a soldering iron. Components are pushed into the sockets on the breadboard and then extra 'jumper' wires are used to make connections.
If you were to pull the self adhesive backing off the back of your breadboard, it would look something like this.
The middle section of the board has two columns, each with 30 strips of connector, like the one pulled out and to the side of the breadboard. These connect together anything that is pushed through from the front into one of those five holes.
On either edge of the board are much longer sections of clip that join together the columns of holes marked by the blue and red lines on the front of the breadboard. These are generally used for GND (blue) and 5V (red).
This is the breadboard layout used in lesson 2.
There is a red jumper wire going from the 5V socket on the Arduino to one of the long power connectors on the breadboard. The resistor has one lead pushed into one of the holes on that 5V red column. The resistor's other lead goes to one of the rows on the right hand side of the board in the center of the board.
The LED spans another connector on the same row as the resistor lead (connecting them together) and the blue (GND) long connector on the right of the breadboard. This long blue GND strip is connected near its top to the GND connection of the Arduino.