The reason a TV is called a boob tube is because the boob is referring to the lazy person who sits around and does nothing or hardly nothing but watch the TV.
It's called a tube because of the older style TV's that used a CRT tube to display the picture.
So the meaning of a boob tube is a TV that a Lazy person watches.
Boob is a lazy person that stares at the TV all day.
The word boob has also been associated with stupidity or easily distracted (hence the slang related to women's mammaries and the term "booby trap").
In British and Britain the word boob tube also refers to a woman's tight-fitting strapless top made of stretchy material; a tube top.