When a quadratic function is graphed, it forms a parabola, a u-shaped curve that has to meets certain technical mathematical requirements. Think of the narrow curve at the end of an oval and you can imagine a parabola.
Imagine a traffic cone. If you look at it from the side, it looks like a triangle. Now imagine a plane, like a sheet of metal, slicing through the cone and parallel to one of the sides. If the plane is removed and the cone turned to that side, the edges of the sliced area would form a parabola. This curved shape is the path followed by something as it moves through the air and is affected by gravity.