Aereo is a company that setup 1000s of DVR's with 1000s of antennas on a New York City rooftop. They lease access to these DVRs for roughtly $5/month and the DVRs stream to your computer.

In the US, broadcast channels are free over the air. However, there is a law that says if cable companies want to retransmit the broadcasts, the networks can charge the cable companies.

Is Aereo "retransmitting" the broadcast, or just renting personal antennas? That is what the Supreme Court was deciding.