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Attached are two pictures of my hot water heater and the ball valve in question. I noticed the other day that the pvc pipe running out of the house was dripping 3-4drops/sec. It's not coming from the pan but from the little tube in the picture. The tube comes from the ball valve on the water inflow and runs down the pipe outside the house. The question is what is this and what to do?

Ice maker line?

Nah. Don't have one. That small tube runs directly into that pvc pipe and the pipe runs out of the house. It exits the house right next to the pipe that drains the pan.

Looks like their way of insuring that the pipes to the water heater don't freeze.

I believe that's called a pop off valve. Call someone like Carr plumbing supply in Jackson and tell them it's leaking and see if they can tell you how to replace it.

Pop off valve is part of the water heater. That's not what that is.
And I don't know what the heck they were accomplishing with that setup.

So the tube is connected to the ball valve? As in the tube is carrying water? The valve that is wrapped with insulation, is that the main shutoff valve or a secondary shutoff valve? If a secondary shutoff valve and the main is directly on the tank, the little tube could be a place to bleed pressure trapped between the two shutoff valves. If there a 3rd valve connected to the little tube, say a little 1/4" valve?

Yeah I would be willing to bet that is a bleeder line for trapped air, but Ive never seen one setup like that. Looks like its there to take the pressure off the valve so you don't blow the valve connection lose....strange set-up

Off the side of your shut off valve on discharge side, you will see a spring loaded valve with the drain line coming off of it. It has a screw insert on the side. Tighten down(if you can) on this valve a little and leak may go away. I had the same problem and turned water off at valve and unscrewed the "screw" and cleaned the spring and seal and used a little "plumber's greese" and stopped leak completly. Good luck.

If the water is hot, then you dont need to heat it. It is a water heater, not a hot water heater. I know... I am a smart booty... ;0)