Since my own explanation of fractals & their nature is fairly basic, I wanted to include some links to several wonderful educational sites that I think you might find useful.
TECHNICAL EXPLANATIONS / DEFINITIONS:
A series of lessons from Yale University with many illustrations--starts simple and gets very complex. BIOGRAPHIES: One of the founders of fractal geometry, Benoit Mandelbrot. Another founder, Gaston Maurice Julia.
ORGANIZATIONS:
http://classes.yale.edu/fractals/
http://en.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot