Power supply voltage confusion
The board has a voltage regulator which converts 9-12V to the 5V that the chip uses.

Why does it need 9V if the board works at 5V? Well, it doesn't need 9 exactly, but it needs something greater than 5. The reason for this is that the regulator has whats called a dropout voltage.

Looking at the schematic of the Uno we see it uses a NCP1117, which has a dropout of 1.2V. So the minimum voltage you can give it to get 5V is 6.2. 

The 9V pin is the Vin pin which is at the same level as the input voltage (before converting).