The reason that it can light up when both ends are touched is that there is nearly always a differance in electrical potential between diffferant parts of the human body.
This device is so sensitive it can pick the differance up and illuminates.
The electrical properties of the human body are extremely important in medicine, for example in an electrocardiograph.
The electrical signals that represent the heart muscles operating are extremely small by the time they reach the skin, where the sensor is placed.
Unfortunately the human body acts like a large antenna, and picks up all sorts of electrical noise generated by things such as flourescant lights, or even just the magnetic fields emenating from wiring installed in the electrical distribution network of any building. These recieved signals are nearly always far larger than those picked up in the skin surface that show electircal activity in the body.
The way to filter it out is to assume the whole body picks up the same electrical noise, but as you get further on the body away from the heart, the detected signal from it will diminish.
By using two sensors, one near the heart and another some way off, and then mixing them in antiphase, or opposition to each other, the unwanted electrical noise cancels itself out, and the heart signal, although reduced, still remains and can be amplified.
The reality is that in practice, five or six sensors may be used, and this all helps to cancel the excess environmental electrical noise, and also to cancel the electrical noise the nervous system itself produces.
In electronic terms, what we are doing is using common mode rejection, ie a similar signal applied to the two inputs of an op-amp will result in a zero output, since they can be configured to work on the voltage differance between them.
Your screwdriver can detect the differances in potential between points on a live human, but on a dead one there would be no potential differance between points.
Dead = no electrical field, no screwdriver lighting up.