This is a marketing thing and nothing more. Solar power is clean, but the stuff you have to build to collect it is not. Just like batteries, it is extremely damaging on the environment. Plus you destroy large areas of vegetation, that produced oxygen and captured CO2. It would have been better if they planted a forest and invested a couple of their billions in a nuclear power plant, which is what humanity is going to have to rely on in the next few decades until we can achieve nuclear fusion.
I agree that we really need to consider nuclear - all power generation has very serious downsides, and when you compare the certainty of global warming to the possibility of nuclear accidents it's pretty clear that nuclear is the lower risk.
However, I doubt that any batteries are involved.
Most solar installations in the US today are grid-connected - they offset the power use from the grid rather than attempt to independently power the facility.
This is an excellent idea, since a major problem for many utilities is dealing with mid-summer mid-afternoon peak air conditioning loads. Since mid-summer mid-afternoons are exactly when PV (photo-voltaic) solar systems produce the most power, they're great for reducing the peak power on the grid.
I have a large (8.5 kW) PV system on my roof. During the mid-afternoon, it sends about 7 kW into the grid (and I'm credited for the mid-day $.32/kWhr rate for that). At night, I draw from the grid at the off-peak $.08/kWhr rate. (Our electric rates are time-of-day based - 8¢/kWhr from 21:00 to 10:00, 15¢/kWhr from 10:00 to 13:00 and 19:00 to 21:00, and 32¢/kWhr from 13:00 to 19:00.)
At the end of the year (with solar, we get yearly electric bills, not monthly), my electric bill will be $0. Although I will have consumed somewhat more kWh than I've produced, I've been selling kWh to PG&E at 32¢/kWh during the days, and buying kWh at 8¢/kWh during the night.
So, Apple's PV system in North Carolina probably won't power the data center outright - but it may help the NC utility with peak summer daytime loads, and help reduce Apple's operating expenses.
And lower operating expenses for Apple should mean lower prices for Mac computers, Iphones, Ipads and other Apple products.