Prolly a little late since school's out now...If you draw a point on a piece of wax paper, and then draw a line, you can fold the line so that it's ovelapping the point. If you do this a enough times at enough different places on the line, you will get a parabola. The dot is the focus, and the line is the directrix.
Not sure if this is really a "real world application" but it would suggest that one exists. Parabolas are useful for many things, and people knew about this before they had computers. They had to draw it somehow, and the directrix was probably a very convenient way of accomplishing this.
That's my conjecture on the subject.
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