Used facetiously, the bozo bit is a notional semaphore flag that you can set alongside your mental model of a person or other entity. Like any other bit in the field of computer science, a bit is Boolean, meaning that it may have one of two states: ON or OFF. By default, we normally assume that any person we meet is not a bozo. This maps well to the common programming convention that new Boolean variables are initially set to zero, or off. Bozo, of course, was a famous TV clown, but "clown bit" lacks the alliterative appeal of the alternative. (Ahem.)
In the course of interacting with another person or entity, we may decide that they are irredeemably stupid or foolish. If we do so, then we set the bozo bit to TRUE. That tells us that we may confidently ignore all future contributions by that person as irrelevant, uninformed, and worthless. Of course, that's a horrible and perhaps even dangerous thing to do. Even a stopped clock is right twice a day, and so on. Not to mention the negative team dynamics that it's likely to foster. But the sad fact is that it's human nature to categorize like this, and once you have slotted someone into the bozo category, it's going to take something dramatic to change your mind.
The term is generally held to originate in the classic work Dynamics of Software Development, where the author urged readers to be aware of the human tendency to make this sort of judgment, and not to do it.