The name of the valve and pipe above is temperature and pressure relief valve. The one in the picture is on the side. However, they may also be found on the top of the water heater. It is a safety valve. When the pressure in the tank of the water heater gets too high it allows water and pressure to be released to prevent the tank from exploding. Yes water heater can explode!
If this valve is dripping water, do not plug it. The valve is doing what it was designed to do: release pressure. You should have your local plumber inspect the heater and valve. The problem could be caused by a bad thermostat or gas valve or it may simply be that the temperature and pressure relief valve is worn and is stuck in the open position allowing water to weep out.
The temperature and pressure relief valve can be replaced if the old one has gone bad.
The temperature and pressure relief valve should be inspected for proper use every year. You can test this valve by manually opening it to make sure that it is not stuck in the closed position. After briefly opening it, make sure that it closes properly. If it continues to leak, you should replace the valve.
WARNING: Before testing the valve, make sure that no one is close the discharge pipe. The water that will be released will be very hot and may cause scalding.