the person with the floor?

[Torsten]

Is "the person with the floor" or what does the phrase in the following sentence mean:

He was always reading, never looking at the person with the floor, and missed nothing.

TOEIC short conversations: Two patients talk about their health problems

[Jamie (K)]

In a meeting, the person who has the floor is the person whose turn it is to speak. We say, "Please stop interrupting! Mr. So-and-So has the floor. I'll give you the floor after he's finished," or, "I'll now hand the floor over to my colleague, so that he can explain the project."

Don't ask me why "floor".