Cars run on an internal combustion engine, where a flammable liquid is ignited in engine cylinders, pushing pistons and powering the engine. When the piston has been pushed, the smoke generated is thrust out of your car through its exhaust system and finally through the tail pipe. It is not uncommon to see water and smoke coming out of the tail pipe for a variety of reasons.
One cause of water coming out of your tail pipe, especially on early mornings, is simple condensation. Overnight the exhaust system's metal cools down to the ambient temperature. When you start your car, it rapidly becomes much hotter than the air surrounding it. The result is condensation forming around and inside of the exhaust system and tail pipe. This liquid is then pushed out with the exhaust and gives the appearance that your car is leaking water.
When the engine turns over quickly, it may expel what appears to be unusual smoke coming out of the tail pipe. This is most likely steam from the exhaust manifold heating up and vaporising the liquid condensation that can build up in the exhaust system. What you could be seeing is water vapour being expelled from the tail pipe.
Smoke While Running
Your exhaust system is designed to carry the exhaust, or smoke from combustion that has already been used by the pistons in the engine, out through the tail pipe. While exhaust isn't typically obvious as it's expelled from the car, especially if the vehicle is equipped with a catalytic converter, if the temperature is cooler, the exhaust may just be more apparent. This is the same effect as when you can see your breath when it is cold outside.
White Exhaust at Normal Operating Temperature
If the exhaust is consistently emitting white smoke when it is not cold outside, and continues or starts after the engine has been running for a while, there could be a problem with your engine's cooling system. To be sure, you should consult a mechanic.