Example of non-perspectival Art:  Bayeux Tapestry
Example of perspectival Art:  "The Last Supper"

Encyclopedia Britannica:
Perspective:  method of graphically depicting three-dimensional objects and spatial
relationships on a two-dimensional plane or on a plane that is shallower
than the original (for example, in flat relief).

Perceptual methods of representing space and volume, which render
them as seen at a particular time and from a fixed position and are
characteristic of Chinese and most Western painting since the
Renaissance, are in contrast to conceptual methods. Pictures drawn by
young children and primitives (untrained artists), many paintings of
cultures such as ancient Egypt and Crete, India, Islam, and
pre-Renaissance Europe, as well as the paintings of many modern artists,
depict objects and surroundings independently of one another--as they
are known to be, rather than as they are seen to be -- and from the
directions that best present their most characteristic features. Many
Egyptian and Cretan paintings and drawings, for example, show the head
and legs of a figure in profile, while the eye and torso are shown frontally
(see photograph). This system produces not the illusion of depth but the
sense that objects and their surroundings have been compressed within a
shallow space behind the picture plane. (see also Index: Egyptian arts
and architecture, ancient)

In Western art, illusions of perceptual volume and space are generally
created by use of the linear perspectival system, based on the
observations that objects appear to the eye to shrink and parallel lines
and planes to converge to infinitely distant vanishing points as they recede
in space from the viewer. Parallel lines in spatial recession will appear to
converge on a single vanishing point, called one-point perspective.
Perceptual space and volume may be simulated on the picture plane by
variations on this basic principle, differing according to the number and
location of the vanishing points. Instead of one-point (or central)
perspective, the artist may use, for instance, angular (or oblique)
perspective, which employs two vanishing points.

Another kind of system-- parallel perspective combined with a
viewpoint from above--is traditional in Chinese painting. When buildings
rather than natural contours are painted and it is necessary to show the
parallel horizontal lines of the construction, parallel lines are drawn
parallel instead of converging, as in linear perspective. Often foliage is
used to crop these lines before they extend far enough to cause a building
to appear warped.

The early European artist used a perspective that was an individual
interpretation of what he saw rather than a fixed mechanical method. At
the beginning of the Italian Renaissance, early in the 15th century, the
mathematical laws of perspective were discovered by the architect
Filippo Brunelleschi, who worked out some of the basic principles,
including the concept of the vanishing point, which had been known to
the Greeks and Romans but had been lost. These principles were applied
in painting by Masaccio (as in his "Trinity" fresco in Santa Maria Novella,
Florence; c. 1427), who within a short period brought about an entirely
new approach in painting. A style was soon developed using
configurations of architectural exteriors and interiors as the background
for religious paintings, which thereby acquired the illusion of great spatial
depth. In his seminal Della pittura (1436; On Painting), Leon Battista
Alberti codified, especially for painters, much of the practical work on
the subject that had been carried out by earlier artists; he formulated, for
example, the idea that "vision makes a triangle, and from this it is clear
that a very distant quantity seems no larger than a point."

Linear perspective dominated Western painting until the end of the 19th
century, when Paul Cézanne flattened the conventional Renaissance
picture space. The Cubists and other 20th-century painters abandoned
the depiction of three-dimensional space altogether and hence had no
need for linear perspective.

Linear perspective plays an important part in presentations of ideas for
works by architects, engineers, landscape architects, and industrial
designers, furnishing an opportunity to view the finished product before it
is begun. Differing in principle from linear perspective and used by both
Chinese and European painters, aerial perspective (q.v.) is a method of
creating the illusion of depth by a modulation of colour and tone.