I only know about this from reading Mark Twain's "Tom Sawyer," describing the behavior of teenaged boys in the mid-1800s. Two boys have taken a dislike to each other. They are "spoiling for a fight." They are daring each other to fight: “That’s a lie.” “Your saying so don’t make it so.” Tom drew a line in the dust with his big toe, and said: “I dare you to step over that, and I’ll lick you till you can’t stand up. Anybody that’ll take a dare will steal sheep.” The new boy stepped over promptly, and said: “Now you said you’d do it, now let’s see you do it.” Drawing a line and daring somebody to step over it is a way of intentionally starting a fight. So, figuratively, "drawing a line in the sand" (or dust or dirt) means to set a boundary, with two implications: a) you will fight anyone who steps over it, and b) you are testing, daring, or challenging them to do it.

Usually, it means to set a boundary of some kind with regard to some kind of interpersonal conflict. It could also be used for political or international conflicts. It's similar to the concept of a red-line. It's the idea that a line has been drawn that shouldn't be crossed by the other party. Usually, it will be 'a line,' but sometimes it can be expressed as 'the line' if it's referring to a specific conflict rather than a general/more figurative one. Sometimes it will be 'sand' and not 'dirt,' also. 'Because of her husband's excessive spending, she drew a line in the sand.'