Perspective is an art technique for creating an illusion of three-dimensions (depth and space) on a two-dimensional (flat) surface. Perspective is what makes a painting seem to have form, distance, and look "real". The same rules of perspective apply to all subjects, whether it's a landscape, seascape, still life, interior scene, portrait, or figure painting.
Perspective in Western art is often called linear perspective, and was developed in the early 15th century. The system uses straight lines to plot or figure out where things must go. (Think of it as light traveling travels in straight lines.) The Renaissance artist Leon Battista Alberti and architect Filippo Brunelleschi are credited with the "invention" of linear perspective.1 Alberti set out his theory in his book On Painting, published in 1435. We're still using Alberti's one-vanishing-point system today!
Perspective is possibly the most feared aspect of learning how to paint. The mere word "perspective" makes many a hand tremor. But it's not the basic rules of perspective that are hard, it's the consistent applying of the rules to every bit of a painting that's hard. You need to have the patience to check the perspective as the painting progresses, and to take the time to fix it. The good news is that learning perspective is like learning how to mix colors. Initially you have to think about it all the time, but with practice it becomes increasingly instinctive.
There is fair bit of terminology used in perspective, and if you try to take it in all at once, it can seem overwhelming. Take it slowly, one step or term at a time, and get comfortable with a term before moving on to the next. That's how you master perspective. Let's start with viewpoint...
1. Alison Cole. Eyewitness Art: Perspective. Dorling Kindersley, 1992. Page 12