For an off-grid house you might like to power it with solar or wind power. Unfortunately, neither of these two sources provide constant energy. If you could store the energy in a battery, you could use this during the night or calm weather.
Many people keep a gasoline powered generator for their house. I have one that I don't use too often, but it's awesome when you need it. What if you had a battery that you could use for your house in times of power outages? That would be cool.
It seems like the power company would like everyone to have a battery. With a house battery, you could reduce power spikes on the grid. When you turn your air conditioner on, it draws a large current for a short period of time(here's an explanation of why the current spikes). With a battery this current demand could be leveled out (I guess).