A pyramid is any man-made structure where the upper surfaces are triangular and converge on one point. The base of a pyramid may be either quadrilateral or trilateral, meaning that a pyramid may have either three or four vertical sides, but all pyramids must have trilateral sides. The measurements of these triangles uniformly classify the shape as isosceles and sometimes equilateral.
A pyramid's design, with the majority of the weight closer to the ground, means that less material higher up on the pyramid will be pushing down from above. This allowed early civilizations to create monumental structures by basing the construction off of the mathematics of a pyramid. Indeed, for thousands of years, the by far the largest structures on Earth were pyramids: first the Red Pyramid in the Dashur Necropolis and then the Great Pyramid of Khufu, the only remaining Wonder of the World.
The largest terrestrial structures on earth, mountains, are fundamentally pyramidal in shape. This is because the pressure exerted on the base of a rectangular or cube-shaped structure is much higher than the pressure exerted on the base of a pyramid. On a cube, the center of gravity is centered. This means that the top half of a cube is just as massive as the bottom half, and so pressure is equally distributed. In a pyramid, the center of gravity is much lower, because the majority of the mass is toward the base and there is an exponential decay of mass higher up on the pyramid. Thus, it was not until the advent of modern building materials that cubic buildings were possible to build on the scale of pyramidal ones.