How to power both arduino and 1 color led strip from single power source
Note that VIN pin and the 2.5mm DC Jack are connected. So in the tutorial one of these is getting power from a +12Vdc source and the other is supplying +12V to the +12v labeled pin on the LED string. Where the R G and B pins of the strip should be connected to Collectors of NPN's. Each of the NPN's bases are driven by Arduino Output pin and all the Emitters are connected to Ground. 

So +12V supplies the DC Jack (aka Vin) the Arduino's local regulator converts that to Ground. The +12V via Vin supplies the LED's. And the Digital Outputs drive the base's of the NPN's. Which in turn act like a relay closing the perspective LED's to Ground, so they can illuminate. Where a Digital ONE or HIGH or TRUE on the BASE results in 5V above ground, which causes it to have low resistance.