How does the RFID-based U.S. passport card work?

The RFID chip will broadcast a number that is uniquely tied to you when it enters a radio field.  The Department of Homeland Security (DHS) uses that number to look up your personal information record that is stored on their servers.  Border officers will then compare you to the record to determine if you should be admitted.  No personal information is stored in the RFID chip.