The term port side originated from the fact that ships used to dock with their left side facing the port (or harbor). This made it easier to load and unload cargo, as well as for passengers to board and disembark. It's a tradition that's stuck, even though ships don't always dock with their left side facing the port nowadays!
In the old days, ships didn't have engines or propellers like they do today. Instead, they relied on sails and wind to get around. The port side was also the side where the ship's wheel was located, making it the "driver's seat" of the ship! Can you imagine steering a massive vessel with just a wooden wheel and a bit of rope?