The Stagefright vulnerability is a remote code execution exploit that can be triggered by sending a malformed media file via MMS. It affects Android phones using default SMS clients like Google Hangouts or Messenger, and can allow hackers to gain access to the device's microphone and camera, as well as copy data or delete it. To mitigate this threat, users can disable automatic downloading of media files sent via MMS by going to the Messages app settings on their device. This will prevent an attack from automatically executing on the phone, but does not fix the exploit entirely until a patch is released.