"Draw the line" is an English expression used to describe the setting of a boundary, usually for behavior, expense, patience, or some other personal expression of patience. It is intended to convey finality in terms of what the person speaking it will allow before responding to correct the situation. This phrase is closely related to the similar idiom "draw a line in the sand", which has a much more antagonistic connotation than the simple form of the phrase. The origins of "draw the line" are a bit cloudy, since there are references to it in terms of both sporting events and war dating back hundreds of years.
An idiom is a simple phrase or expression with a meaning that has grown through popular usage far beyond the literal meaning of the words. For example, when someone says that she has a broken heart, she does not actually have a broken heart. Instead, she is making a colorful reference to a state of sadness. Idioms are used for practically every aspect of life, and they allow for speakers to communicate with other members of their culture who are aware of the intended meaning of these phrases. "Draw the line" is one such particularly powerful idiom.
When someone uses this specific idiom, it means he or she has become fed up with some situation and is finally setting up boundaries. The implication is that there is a limit to which the person will allow the situation to go, and he or she will allow it to go no further. For example, a parent might say to his children, "You can go out until 11:00, but then you have to come home, because that is where I draw the line."
From the phrase "draw the line", another idiom, "draw a line in the sand", has emerged. Their meanings are similar, but "draw a line in the sand" generally has a bit more menace attached to it. The implication with "draw a line in the sand" is that a person is ready to react with severity should anyone try to cross that imaginary line. For example, consider the sentence, "He drew a line in the sand concerning his expectations, and no one dared to cross it."
It is difficult to pinpoint the origins of the phrase "draw the line." Boxing and tennis, in the distant past, both required the actual drawing of lines to set boundaries for the competitors. As for "draw a line in the sand,", there are references to it in war accounts dating back as far as the Roman Empire.