Visual example
The following image shows the shape of a parabola. Said another way, the curve is parabolic.
Algebraic Form
An equation that graphs a parabola takes the following form:
$$ y=Ax^2+Bx+C $$A quadratic equation has the shape of a parabola when graphed.
Properties of a parabola
A parabola extends to infinity in direction, but does not extend to infinity in the other direction -- it has the shape of a U. The point right at the tip of the parabola is called the vertex. It also has a focus (a single point inside the parabola) and a directrix (a line perpendicular to the parabola). The parabola consists of all points equidistant from the focus and the directrix.