Water conducts electricity fairly well (due to the presence of dissolved ions in it). So from the point of view of electric current water is something it can run through. And since water tends to leak everywhere it is likely to be in contact with further conductors.

Electricity flows in a loop - a complete circuit back to the power source. With a battery, yiu have to have a wire going to both ends of the battery to complete the loop.

Water conducts electricity, so it acts a bit like a wire. Electricity will always take every possible path to complete its loop. Electrical wires are designed with insulating covers (plastic) over the surface of the metal specifically to keep the electricity only in the wires. But in water the electricity can spread out.

Now imagine that if you put a bare metal wire in water. The electricity will try to flow through the water on all directions to find the loop that completes the circuit.

Often the loop is quite vague - especially in mains power. The power plant produces power, and normally the loop is two separate wires on your electrical cables. However, there are other loops possible - the electricity can go through a pipe into the ground, the through the ground back to the power plant and the back into the generator through a ground wire.

So if you drop a hair dryer on the bath, bare wires inside the hair dryer get exposed to water. The water spreads out through the water looking for a loop. It finds the drain pipe which goes into the ground and that gives it a path back to the power plant.

Now you reach in to the bath to pick up the hair dryer. You have one hand on the metal bath tap and yih reach in with the other. Your body conducts electricity and when you reach in, the electricity finds a new loop from the water-through your arm, then body, then down into the tap, then into the water pipes. So, some of the electricity flows through you and that is why you get shocked.

Shortest correct answer:

Water conducts electricity, but your skin conducts it better.

Put baking soda in the water and it becomes VERY conductive. Stick 2 electrodes in and the charge will go around you and rapidly boil the water instead.

Underwater welder here; actually fresh water does not conduct electricity very well but salt water does because the dissolved salts (sodium, magnesium and potassium salts) are electrolytes, meaning they have the ability to conduct electricity. Our bodies need electrolytes for our nervous system to function so we are slightly salty; think of our blood, sweat and tears. When immersed in fresh water (like a bath tub), any electrical current "sees" our body as a better conductor than the fresh water so the current would prefer to travel through our body than the surrounding water. Put bath salts in your tub and now our body is less of a conductor (but stray electricity can still give you some tingles).