For a detailed and very well written answer to “What’s a Fractal”, have a look at the Wikipedia entry.
As for the “Why should I care?” part of the question, let’s have a very short look at what a fractal is and then discuss how they apply to Terragen 2:
- A fractal is a geometric shape that looks approximately the same no matter how close in or far away you are, and it maintains fine structure at all scales. This is called self-similarity.
- Fractals conveniently also often look like things in nature (clouds, mountains, thunder, frost crystals, …).
- Fractals can be represented by a (usually straightforward) mathematical formula.
Terrain rendering software can use those three properties to draw landscape that is convincing both close in and far away. Certain fractal formulas look just like mountain ranges both close in and far away. The program just needs to evaluate the formula for the area being rendered. Need to draw a cloud? Other fractal formulas make convincing clouds. Just evaluate that formula to get a cloud. Want to zoom in really close to the mountain? The self-similarity property ensures it will look pretty convincing.
To see a simple case of fractals in action, consider the Von Koch curve. It’s created simply by drawing a triangle, then taking each edge of the triangle and inserting the tip of another triangle. Then take each edge in the resulting shape, and insert the tip of another triangle. That can be repeated indefinitely. If you do that 100 times and then zoom in on a small segment, it will look pretty similar to how it looked after you did it 2-3 times. Here’s an example:
Fractals are used in many parts of Terragen 2. Hopefully this brief overview (and the Wikipedia article if you have the time) will give you a better understanding of just what they are.