It's not just about making sure our cell phones last a little longer, though that's a nice side-effect too. Really, what's going on is that the new wave of wearable devices, flying drones, electric cars, and what-have-you are going to have higher and more specific power needs than what you get with our current lithium-ion (like in phones) and alkaline batteries (like in Wii controllers).
It's the same reason Tesla and IBM have their own battery research efforts, too.
So take for example solid-state, thin-film batteries, which offer better battery life while still being thinner and lighter than our existing batteries. They're currently expensive and hard to make a lot of them, but they'd be perfect in the next generation of smartphones.
But as the report notes, they're also perfect for Google Glass, since the better battery life helps with stuff like video, which can sap a lot of power.
And perhaps more importantly, these solid, thin batteries are ideal for powering cutting-edge computing like Google's glucose-monitoring contact lens, since there isn't horrible flammable acidic juice at the core as there are with today's batteries.
In the future, computers aren't just going to be a part of our lives, they'll probably be a part of us. Intensive wearble devices and even implantable devices leave concern for health. Nobody wants to have an implantable device with a leaky battery. This is one thing Google is focusing on to prepare for the future.
Meanwhile, lithium-ion batteries are still not great for stuff like Google Loon, the Internet-broadcasting balloon relays that Google is testing for the developing world. Traditional batteries freeze at high temperatures, and so Google X engineers are coating them in blends of wax and graphite in a way that makes the heat diffuse more evenly.
It's worth noting that Google's other secret research lab, the Google Advanced Technology and Projects (ATAP) lab led by ex-DARPA chief Dr. Regina Dugan, once scrapped a project that would improve mobile battery life by five times.
Which is to say, getting better battery life isn't as easy as it may seem. Our computers are getting faster and more powerful by the year, but the batteries that power them just aren't keeping pace.