Just as a line is made of an infinite number of points, a plane is made of an infinite number of lines that are right next to each other. A plane is flat, and it goes on infinitely in all directions. A sheet of paper represents a small part of one plane. But actually a sheet of paper is much thicker than a plane, because a plane has no thickness. It is only as thick as a point, which takes up no space at all. So a plane is like an imaginary sheet of paper, infinitely wide and long, but with no thickness. If you looked at a plane from the side, it would look like a line.
When we talk about a triangle, or a square, these shapes are like pieces cut out of a plane, as if you had cut them out of a piece of paper. You can make a triangle by choosing any three points on a plane and connecting those points with line segments. The part of the plane that is in between those lines is a triangle. To make a quadrilateral, you choose four points instead. To make a circle, you choose one point to be the middle of your circle, and then draw all the points that are at the same distance from your first point, and the part of the plane that is between those points is a circle.
When we make a solid shape like a pyramid, we do that by stacking up lots of planes - an infinite number of planes - side by side, like a stack of paper. The shape of the solid depends on what shape pieces we cut out of each plane.
To find out more about geometry, check out these books from Amazon.com or from your library: