To summarize if a port is open drain (or open collector) then that port connects to GND for logic 0. For logic 1 the circuit remains open. This enables connecting a relay, designed to be operated at 12 volt, to port 0 pins even though the chip is working at 5 volt.
This way output load is activated when there is logic 0 on the pin. In case internal load resistors are present then external load will be off for logic 0. This will keep the current to flow through the pull down transistor. This is one disadvantage of having the pull up resistor.