Why would a magnet conduct electricity?
Many magnets are capable of conducting electricity. This is because many magnets contain iron, which is a good conductor of electricity.
Whether or not a magnet can conduct electricity depends entirley on the material of which they are composed. If its a metal magnet, then more than likely, albeit poorly. A magnet can CREATE electricity, by inducing movement in the electrons of a copper wire, as you can see in a generator (copper wire coiled into a cylinder with magnets moving perpendicular to the coil)
Assuming you mean electrical conductor / insulator, most bar magnets are made of solid metal, either iron, neodymium or an alloy of aluminium nickel and cobalt, so they conduct electricity. There is one type of magnet called a ferrite magnet which does not conduct electricity - they are the type often found in loudspeakers.
I'm guessing this question stems from the fact that water conducts electricity well. This is actually a misconception. Pure water does not conduct electricity at all. It is only the impurities in water that conduct electricity. Even if it did conduct electricity, there would still be no shock because it only conducts electricity, not generates it. If there is no generator, there is no electricity. The other possibility is that this question comes from the…
Volt Metre is the apparatus used to detect the electricity generated. Moving a magnet in or around coil of enamelled copper wire or vice versa will generate electricity. The electricity generated can be detected, by connecting the ends of wires of coil to a Volt Metre. The Voltage generated proportional to the speed of movement and strength of the magnet, and the number of turns of the coil.
Some magnets conduct electricity quite well. Others are pretty good insulators. If the magnet is made from metal, chances are that it will be a pretty good electrical conductor. If it is a ceramic magnet or one where magnetic particles are suspended in a non-conductive medium (like those flexible rubber fridge magnets that businesses like to distribute) then the magnet will usually be a very poor electrical conductor.