Since we began drawing images that we perceive in the real world on flat walls and other such surfaces, we have learned the skills necessary to translate what we see with two eyes to a flat surface which is a fixed, monoptic view. Whether we did this by eye or by mechanical device our job was to translate the visual world to its simulation on a surface with height, width and very limited depth. We shall make exception of the bas-relief created by textured medium, as it is not a concern of this short summary.
We are accustomed to walking around our subject. As we move, our two eyes work in unison to give us an idea of not only the height and width of things, but their distance in space from us. On a flat surface, such things change much less. For some time for instance, people such as Jules de la Gournerie wondered why a painting of a person that seemed to be staring straight ahead also seemed to follow the viewer no matter what angle the painting was viewed from. This is one of the many illusions possible when converting the third dimension to a flat surface.
The artist can choose to emphasize the third dimension, or to find a flat pattern to focus on. In the first image below, the green trees form a somewhat flat expanse. covering the scene from right to left and up and down forming a wall of sorts. There are subtle clues in the layering of the colors and their transparency differences as to the layering going on in space.
In this second example of a rock sculpture, the perspective as well as the placement of the stone sculpture in space, heightens the sense of distance in an exaggerated way. Many other devices than perspective are at work in this photograph including the diminution of value and color. The presence of a horizon line is a strong factor contributing to the success of perspective in pulling the viewer back towards the distance.
In the study for the famous painting "A Sunday On La Gande Jatte" (1885) Georges Seurat places the one point perspective to the right of center side similarly to the stone sculpture. The placement of the eyes of all of the figures near to the horizon line establishes the viewers (our) vantage point to be common with the rest of the standing figures. We could be there on the grassy hill with them. Even though the forms are slightly abstracted there is a definite feeling of space conveyed by the repeated shapes of the figures that scale down in size with the perspective. We recognize such relationships and consistent patterns of change suggest the ordered rules of perspective as they play on the flat visual plane similar to how they interact with a single one of our retinas. The frame looks as a shadowbox window with suggested depth.
In the illustration at the top of this article there is an image of an artist using a physical device to capture points of perspective as they pass through a flat grid in an attempt to make a physical measurement in space and convert to a perspective plane. As photography became available, such devices became less useful and therefore less common in comparison to newer technology. The camera and the eye still operate on the same principles, where the beams of light function in the same way as the strings of the perspective device.
A cube in two-point perspective (above).
It wasn't until around 1420 that Brunelleschi rediscovered the lost art of perspective. The video below tells a little bit about Brunelleschi's discovery.