The trouble with hot water tanks is that you always eventually run out of water, even with a decent sized tank. Everyone knows the scenario - you have just run the dishwasher, the washing machine and bathed the kids... now it is time for your own well deserved relax in the tub after a hard day... Only there is no hot water left! This does not happen with instant hot water heaters.
These on demand hot water heaters have only become popular in the US over the last couple of decades, though in Japan and Europe they have been in use for longer. Basically it is a system that allows you to heat your water on demand.
There are lots of ways to achieve this - with gas (natural or propane), oil or even a high tech tankless electric water heater. They all work in the same kind of way, by heating the water as it flows in from the mains. That means that, providing you stick to the specifications, you can have constant, instant hot water for as long as your energy supply and water lasts!
The specifications of instant hot water heaters need to be matched to your home needs - what matters for on-demand heaters is simultaneous demand since they can only heat a given amount of flowing water. In practice this amount can be very large, and most people looking to swap from a sixty gallon home tank should have no difficulties finding a tankless hot water heater to meet their needs.