Angel radio is Dean's nickname for the conversation between angels that other angels can hear. The phenomenon is first named by Dean in 4.09 I Know What You Did Last Summer. Unusually, Metatron also refers to it as "angel radio" in 8.22 Clip Show.
Dean and Sam find Anna Milton, who has escaped from a psychiatric hospital. She describes how she can hear the angels talking. Dean responds: "So, they lock you up with a case of the crazies when really you were just... tuning in to angel radio?"
Metatron sets up a radio in his office to broadcast to all angels on Earth and in Heaven across all frequencies of angel radio to let them know he is traveling to Earth and closing the portal while he is gone. When confronting Castiel in his office, he doesn't realize Castiel has activated the microphone and Metatron's true intentions and opinions of the angels are broadcast to everyone, leading to his downfall.
Upon a Nephilim coming into existence, Castiel is besieged by voices on angel radio, telling Sam and Dean that there has been a massive surge in celestial energy. Which can only mean that Lucifer has sired a Nephilim.