This is what TonyAwards.com had to say about the musical:
'American Idiot tells the exhilarating story of a new generation of young Americans as they struggle to find meaning in a post-9/11 world, in a journey borne along by songs of the band Green Day. The musical follows working-class characters from the suburbs to the city to the Middle East, as they seek redemption in a world filled with frustration. The cast of 19 is led by past Tony Award-winner John Gallagher, Jr.'
'American Idiot' has also been nominated for a couple Drama Desk awards. Director Michael Mayer is up for Outstanding Director of a Musical and orchestrator/arranger Tom Kitt is up for the Outstanding Orchestration award (he is also nominated in that category for the musical Everyday Rapture).
The full list of nominations can be viewed here.