what is a parabola?

The parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.

Given a point (the focus) and a corresponding line (the directrix) on the plane, the locus of points in that plane that are equidistant  from them is a parabola.

The line perpendicular to the directrix and passing through the focus (that is the line that splits the parabola through the middle)is called the "axis of symmetry". The point on the axis of symmetry that intersects the parabola is called the "vertex". The vertex is the point where the curvature  is greatest. Parabolas can open up, down, left, right, or in some other arbitrary direction.