5V power supply negative terminal connection
The Arduino common, normally referred to as ground, although it is usually only accidentally grounded through external connection. In general ALL connections should have a common "ground".

You can not measure voltage across the LED given the circuit you have listed. (You could read the voltage at both ends and subtract.)

If you swap the LED and resistor you can get an approximation of the LED voltage (actually LED + Arduino pin) from the junction of LED and resistor.