What's the purpose of this ground connection circuit?
This is a trick for clipping away small voltage noise coming into a device via the ground line (e.g. ground loop noise) while still providing a ground connection. 

As long as neither diode is forward-biased, the ground is effectively lifted. It's like a voltage-controlled ground lift switch. The switch stays closed against small noises which don't exceed the forward voltage in either polarity.

If there is a fault in the device which causes current to be dumped into the ground, then one of the diodes will spring into action and carry the current. The only problem there is that the diode needs to handle that current without melting.

The "Ebtech Hum X" is rumored to use the same trick.