Slang Jon Stewart often uses for the flu or common cold.
Based on the way he pronounces it (tongue-in-cheek Godfather character accent) it's probably the plural form of the Italian word 'bubbone,' a swollen lymph node characteristic of bubonic plague. It probably developed as slang for an infection because bubonic plague is so infectious. Stewart probably picked it up growing up in the NJ/NY area.
"I have the bubons again. It's the second time in three months. Let me say this to anybody out there with children at home: buy an autoclave."
The Daily Show
February 22, 2011
noun, a severe cold or flu that's kicking your ass, usually caught from kids who bring it home from pre-school.
Made famous by Jon Stewart on The Daily Show.
"Did you see the Daily Show last night? Jon Stewart had the bubons, he could barely interview that guy."
"I can't go out for drinks, I've got the bubons."