The inhabitants of Flatland are two-dimensional shapes, and they can't perceive height, only length/width on the same plane. In other words, every person living on that plane appears as a straight line, regardless of the number of sides they have; they all have varying numbers of sides, except for women, who actually are straight lines. They can perceive colors, but it is difficult to tell the difference between high or low class people because they all appear as lines. This causes difficulty because some of the people have sharper corners, making them dangerous to others.
However, the upper classes practice a type of sight recognition, based on the fog that permeates Flatland. The narrator explains:
I shall see a straight line, in which the middle point (A) Will be very bright because it is nearest to me; but on either side the line will shade away rapidly into dimness, because the sides AC and AB recede rapidly into the fog and what appear to me as the Merchant's extremities, viz. D and E, will be very dim indeed.
(Abbot, Flatland, geom.uiuc.edu)
The accompanying image shows how the sides of a Triangle, receding sharply into the distance, would be less clear than those of a Pentagon. The brightness of the two lines appearing in the fog are what allows differentiation between shapes, and the narrator explains that it takes a lot of study to become proficient in sight recognition. Women, being straight lines, can appear as a line but also as a point, and because of the danger of running into their points, must keep up a peace cry in public so no one will be harmed.