These two snippets from the decision sum up the reasons for the judgement perfectly:
General knowledge that infringement is 'ubiquitous' does not impose a duty on the service provider to monitor or search its service for infringements ... the burden is on the owner to identify the infringement
What Viacom was trying to do, in layman's terms, was attempt to force Google/YouTube into taking the burden of enforcing copyright beyond traditional copyright law and the DMCA. If Viacom prevailed, it would mean YouTube would have to review each and every video uploaded to their site and determine if the video infringes someone's copyright.
This decision is good news, not only for website operators, but also for virtual worlds. As an example of how virtual worlds could have been negatively affected if Google lost, one only needs to look at the long dead virtual world There.com.
There.com residents were split into two classes: consumers and content developers. To become a developer, you had to enroll in the developer program. When you create content, you can't simply start selling it on the spot(like with SL/OpenSim). You must submit the content to There.com's review staff. If the content doesn't pass the review for reasons such as inappropriate content or perceived copyright infringement, you can't sell or use the content inworld.
The problem with this approach is that the review staff weren't copyright owners or authorized agents of copyright owners. Yet they actively played "copyright cops" even in the absence of proper DMCA procedure. This, despite the approach successfully enticing RL companies into creating presences in There, actually endangered their ability to invoke the DMCA Safe Harbor provisions in court.
It's not hard to see that this sort of "copyright police state" scenario is very possible in SL and OpenSim grids, because SL/OpenSim's situation is practically identical to YouTube. Copyright infringements happen quite often in virtual worlds, but it's practically impossible for the grid operators to police the entire grid for copyright infringements. They would wind up dedicating all of their time taking down content they think is infringing someone's copyright instead of properly operating, running and improving the grid. It's an undue legal burden.
That's why the decision states that the burden is(rightfully) on the copyright owner, not the service provider, to identify(via DMCA notices) infringements. The service provider isn't liable to legal action unless they do not follow DMCA procedures. That's Safe Harbor in a nutshell, folks. Be thankful for it.
Update: Via one of my favourite YouTubers, Thunderf00t, I have found a jaw-dropping 18 minute video of Mike Mozart of JeepersMedia catching Viacom doing the exact same thing they accused Google/YouTube of doing. Using Viacom's logic, the YouTubers whose videos got uploaded to Spike.com without their permission could sue Viacom(not the "uploaders"). And since Spike.com(formerly iFilm.com) claimed to "screen all videos uploaded", they may lose Safe Harbor protections under the DMCA. So Viacom, maybe you should rethink filing an appeal, and be happy the judge ruled in Google's favor. You actually benefit from it, believe it or not.