The product that Cablevision offers to its customers allows them to perform normal DVR functions, like recording shows and pausing live TV, without pruchasing or renting an actual hardware device.
Instead, the content is recorded on Cablevision's servers while the user controls the actions of the DVR across the network. The user makes all the decisions about what and when to record, but the actual recording occurs on Cablevision's hard drive instead of a hard drive inside a device in the subscriber's home.
A federal district court judge initially sided with the plaintiffs, but a panel of the 2nd Circuit overturned that decision and held that the copies on Cablevision's servers, since they were only created upon the initiative of the subscriber, fell within the typical fair use exception for home recordings.
The panel also found that a 1.2 second storage buffer was of a "transitory duration" and did not amount to copyright infringement.
While the Court's decision today effectively ends this particular case, don't expect the issue to go away. The parties agreed to take many issues off the table in the case, such as fair use and indirect liability, so expect to see litigation in the future exploring those issues.
Cablevision remote DVR stays legal: Supremes won't hear case (Ars Technica)
Supreme Court Serves Up Remote-Recording Victory (Wired: Threat Level)
The Death of Television Draws Ever Nearer (Gawker)