During a speech at the 5th Annual Energy Storage Symposium, Tesla's Chief Technology Officer JB Straubel gave a keynote speech that was very revealing about how Tesla sees itself and where it sees opportunities in the future. Elon Musk has always said that his reason for creating Tesla and SolarCity was that he wanted to catalyze both the production and consumption of clean energy. It looks like Tesla will have a role to play not only in the consumption part (moving transportation from oil to electricity), but also in the storage of renewable energy, which often comes from intermittent sources like wind and solar. The battery Gigafactory will of course play a big role in that, with a certain amount of its production going to stationary energy storage devices and not electric cars, but Tesla isn't just planning to make battery. It's designing the whole storage systems - which is part of its expertise thanks to its EVs - and plans to scale them up quite a bit.
It's already testing a 2 megawatt-hour battery pack (see below) at its electric car factory in Fremont, California, and plans to scale it up to 4 megawatt-hour within a few months. The current 2 MWh pack is enough to handle 10% of the factory's peak demand, which can lead to savings if you charge it up off-peak when electricity is cheaper.
Straubel's general message about battery technology is that we "should all be thinking bigger". He also said that just in the five years between the Tesla Roadster and the Model S, lithium-ion battery performance has improved by 40%. Over the past 10 years, energy density has doubled. And the best might be yet to come, as Straubel said that the curve is not starting to slow down and plateau yet.