The pipe referred to in the question is the overflow piper linked to the temperature relief valve. It is connected to the water heater. The purpose of this pipe is to ensure safety. It will release any excess temperature or pressure inside the heater caused due to high pressure.
At times it is noticed that this pipe may release steam. It is normal. But if the leakage is constant, it demands a service from expert water heater mechanics as it might cause wastage of electricity.