A parabola is one of a family of curves called conic sections. A traffic cone or ice cream cone is a rough example of a mathematical cone.
Imagine a perfect cone, like a witch's or a wizard's hat with a point. You can cut across it in different ways. If you cut horizontally from one side to the opposite side, you get a perfect circle. If you cut at an angle the cross-section is an ellipse.
If you make a vertical cut you get a parabola. The graph of a parabola in its simplest form is y=x^2. It has a U shape but the arms are splayed outwards moving further apart. The curve can be inverted: y=-x^2, and the U-bend where the curve folds over into its opposite arm is called the vertex, the maximum or minimum point on the curve.
A parabola can be used as the basis for a parabolic reflector on an electric fire. You may have one of these in your home.