Maev already broke it down but i'm going to try to analyze it differently.

I feel this was written to have a deeper understanding of the world, like the reason most of plato's stories were written. but this is different, because he describes how to physically break down the world into sections that can be perceived through logic. By making these "lines" and divisions he tries to simplify the world. if one knew where they were and what exactly was going on, would things be more simple? i don't exactly know all the answers but i do know that plato tried to clearly define the world.