> I have limited knowledge of guns. I understood that they had a physical safety switch that had to be manipulated before the firearm could be used. Is that the case?

Some handguns have manual safety switches, others don't. For example, the Sig P365 (an excellent, highly regarded sub-compact pistol often used for concealed carry), has models with or without a manual safety (you can also install a safety yourself if yours doesn't have one). Some handguns also have a "grip safety" which requires you to firmly hold the grip to disable the safety.

> If so, is the safety left off when people are carrying with a round chambered? Or have I misunderstood the purpose of the safety?

Because modern firearms have a variety of built-in safety mechanisms, separate from manual safety switches, which prevent unwanted discharges, the only thing that will cause a good firearm to go off will be the trigger being pulled. Combining this fact with modern form-fitting holsters which fully cover the trigger guard, it becomes impossible to fire the gun while it remains in the holster. This means that even without a manual safety switch you can carry safely without worrying about the gun going off until you draw and pull the trigger.

Echoing another reply to your comment, if you do have a safety on your gun you would typically toggle the safety while training to build muscle memory. This means you would practice enabling the safety, holstering the firearm, drawing the firearm, disabling the safety, and firing in a swift motion so that you always disable the safety when drawing.