In general, an imaginary line is any sort of line that has only an abstract definition, and does not exist. In fact, is used to identify the map properly.
As a geographical concept, an imaginary line may serve as an arbitrary division (such as a border). It may also be a standardized mark that serves as a measurement or point of reference (such as a circle of latitude or the Prime Meridian).
References
Imaginary line Wikipedia(Text) CC BY-SA