Perspective is a way of showing space in three dimensions. By using perspective, a flat picture can seem to show depth and distance, just as your eye would see it.
There are different ways of showing perspective. Look at the painting Cape Cod Evening by Edward Hopper. Notice how the straight lines on the house seem to move on a diagonal away from you, toward a background point. This is called linear perspective.
Another way of showing perspective is atmospheric perspective. Notice how the dark green area on the left seems farther away than the lighter green trees. That's because light colors “jump out” while darker colors seem to fade away, as if they were farther back in the atmosphere. You also notice the lighter trees more because they have more detail.