The truth is that tankless water heaters are no more efficient at heating water than most traditional water heaters. The difference is that tankless units only heat water when there is a need for it. So when you turn on a hot water faucet, the tankless water heater begins heating water as it flows through the pipes. On the other hand, traditional water heaters run 24/7 to maintain a large tank of hot water. This process is where traditional water heaters waste a considerable amount of energy.
It might not appear to be inefficient to maintain a tank of hot water but think about all of the hours of the day that no one is home and using hot water. Also, consider all of the hours at night when everyone is sleeping and not using hot water. And finally, think of the week or two that you are away on vacation. Every minute of all of this time, a traditional water heater is using electricity or gas to maintain the temperature of hot water that no one is going to use. Switching to a tankless water heater will instantly eliminate all of that waste of energy and money.