A fractal is a geometric shape that exhibits self-similarity across all scales.
The image being generated below is a well known example of a fractal, called The Koch Curve. Each line segment is replaced by the original arrangement over a number of iterations (in this case four iterations). As you can see in the last iteration, no matter how close you zoom into the image, each portion represents the whole shape. If the iterations continued down to the infinitely small, the self-similarity would still be maintained.