A parabola is defined as the set of all points equidistant from a line and a point not on that line.
The line is the directrix, and the point is the focus. The vertex of a parabola is equidistant from both the directrix and the focus. So, for every parabola, there is a line outside of the parabola and a point inside the parabola that are the same distance to every point on the parabola.
Usually, in the equation of the standard form of a parabola, there is a letter p, and the focus and directrix are each p distance away from the vertex of the parabola.
Different books use different equations for "standard form", but Dr. Khan has a good introduction here: