From the FoxNews report of Justice Kennedy's opinion for the court:
The inclusion of a brief, ceremonial prayer as part of a larger exercise in civic recognition suggests that its purpose and effect are to acknowledge religious leaders and the institutions they represent, rather than to exclude or coerce nonbelievers.
And there is something for the Gottesdients Crowd to ponder: in modern American parlance "ceremonial" indicates insincerity. A brief, ceremonial prayer is no big deal. If it's ceremony, then it's not authentic, you don't really mean it. This is perhaps the greatest hurdle to our flocks' understanding of public worship, liturgy, etc, etc.