Ah... The infamous "neon screwdriver."
Scott hit it with the "testee" completing the circuit. Inside the screwdriver handle is a small neon lamp and a series resistor. When you hold the clip and touch a hot terminal you are actually completing the path for the current through your body.
You don't feel anything, because the current involved is very tiny. The series resistor by itself would limit current to a milliamp or so, but the actual current drawn by the neon is in the order of microamps.
It's because the neon is an inherently high-impedance device that it lights even though the resistance to ground via your body might be very high.
You can try an experiment:
Stand on the floor wearing dry slippers or rubber-soled shoes and touch the screwdriver to a hot terminal. It will light, but probably rather dimly. Now take off your shoes (and socks if you like) and repeat the test. You'll find that as the resistance to ground via your feet is now lower that the neon will be considerably brighter.
