The top two rows (and the bottom two rows) are usually used for providing power and ground for all components on the board. Note that each of the whole row (in red box) are connected, and you can power the board by connecting the power source and ground to any pin of the row.
The middle of the board is where you connect components and controllers togethers. Each row can be connected to the other using jumper wires or 24-gauge wire. Note that each column are connected (5 pins of each column as in the green boxes), and each column could be considered the same point in the circuit.
Getting power from Arduino
This circuit only uses the power from the Arduino board directly without using any output pins of the board. Thus no logic can be applied.