Neon screwdriver
Neon screwdrivers are used to test mains circuits to see if they're live. However they have significant problems, and the majority view on uk.d-i-y is they're best not used at all.
How they work
Mains power flows down the screw driving tip to the resistor and neon in the handle. When you touch the brass cap, mains power flows through you, completing the circuit and lighting the neon.
The currents involved are small enough not to feel, so the normal current level is not a safety concern.
The Problems
Direct shock
Water or condensation on the resistor can result in the tool passing higher current to the user, causing a shock, maybe a fall from a ladder, and the slight risk of fatality.
Certain tool faults such as resistor failure can cause the same problem.
False negative
No connection of the human to earth will result in dim lighting on a live wire, and this can go unseen in daylight. The result is shock from touching a live wire, and this is probably the most common failure mechanism.
False Positive
A user capacitively connected to a live supply will light a neon screwdriver touched to any non-live wire. It is quite easy to be capacitively coupled in this way without noticing. Holding an inspection light, standing on a cable, even leaning on a wall in some cases, and so on.
Legality
Because of the issues with these tools, they are illegal to use at a place of work.
Further discussion
Alternatives
The best alternative is a multimeter. A reasonable quality meter will do far more than a neon screwdriver, and do so with more reliable results. Multimeters have their own safety issues, but they are less and much more under the control of the end user, so can be minimised with care.