What is the significance of the term "Line of Demarcation?"
The term "Line of Demarcation" is usually used when referring to the Treaty of Tordesillas. This was a treaty that divided the world up between the countries of Spain and Portugal. This treaty was created and ratified in 1494, just two years after the "discovery" of the Americas by Christopher Columbus.
In this treaty, a line was drawn one hundred leagues west of the Azore and the Cape Verde Islands. Everything to the west of the line was to belong to Spain while everything to the east of it belonged to Portugal. The major relevance of this today is that this is the reason why Brazil was colonized by the Portuguese while most of the rest of the continent was Spanish.