It is hard to see how things are wired up from the photograph but it looks wrong.
On a bread board the outer lines run horizontally and the inner ones run vertically. So on that photograph it looks like you have shorted ground to an output pin. The white wire is not connected to anything. The yellow wire is connected to a resistor to ground and the LED is not connected to anything.
Connect a wire from the output pin 13 to the resistor, from there to the LED and the other end of the LED to ground. Make sure you have the LED round the right way and you have enabled pin 13 as an output in the setup() part of your sketch.