Why does the ADC require 3 wires instead of 2?
The photocell and 1K form a voltage divider, creating a voltage depending on the light. You'll get 5V * 1K / (R+1K) as the voltage on A0. With just the photocell, A0 will be pulled up to 5V so that's no use.

With the wires loose, you're picking up stray AC signals - the wires act as an antenna.