What does it mean that a power supply is 'referenced to mains' and why is that dangerous?
Most power supplies use a double-insulated transformer between the incoming mains and the outgoing extra low AC or DC voltage.  This means that you will not get an electric shock if you touch one of the output terminals.

Some very cheap power supplies do not provide that isolation.  One or other of the output terminal may be at the full mains voltage.  In some cases, it might be safe (well, safeish) with the plug one way round, but dangerous with the plug reversed.

Such power supply designs should never be used for "wall warts".  They should only be totally enclosed within the body of an appliance, and even then only if there are no exposed electrical parts (such as headphone sockets) that the user could touch.