The case was Riley v. California. David Riley was pulled over in San Diego for having an expired registration on his car. The police found loaded guns in his car, and then examined his smartphone.
The phone provided evidence that linked Riley with a street gang and a shooting. Based on this evidence, he was convicted of attempted murder and sentenced to 15 years to life in prison.
Current police procedure law says that, once a person is arrested, the police have the right to search any items they have with them, including in their car.
But, in overturning Riley's conviction, the Supreme Court is saying that cell phones are fundamentally different from most of the things people usually carry on their person. Smartphones contain "a digital record of nearly every aspect of [people's] lives," according to the Court--and it would not be fair to allow police to pry so deeply into someone's life without getting a warrant.
This is a great ruling for anyone who cares about privacy rights and criminal defendants' rights.