Perspective is the technique used to represent a three-dimensional world (what we see) on a two-dimensional surface (a piece of paper or canvas) in a way that looks realistic and accurate, as we see it in nature. Perspective is used to create an illusion of space and depth on a flat surface (or the picture plane).
The rules of perspective applied in Western art as we known them today developed during the Renaissance. Prior to this, there wasn't an expectation that paintings would be realistic, or naturalistic, representations of life. Instead paintings were stylized and symbolic. For instance, the size a figure was painted could indicate their importance relative to the other figures, and individual colors had significance great than their actual hue (see Ultramarine: The Most Expensive Pigment Ever).
There are three basic types of perspective: one-point, two-point, and three-point. The one/two/three refers to the number of vanishing points used to create the perspective illusion. Two-point perspective is the most commonly used.