CY stands for Container Yard.. Container Yard is a place within a port or terminal where containers are stored before it is loaded on the ship in the case of exports or offloaded from the ship in the case of imports..
In some cases in the body of a bill of lading you might have seen a notation CY/CY or in the Port of Loading or Port of Discharge fields in the bill of lading, you might have seen this added after the name of the port, like so (Durban CY)..
This means that the responsibility of the carrier either begins (in the case of Port of Load) or ends (in the case of Port of Discharge) at the Container Yard..