To make it simple, fractals are any kind of fragmented pictures with a certain structure. A fractal set is by the definition of Mandelbrot ment to be any not "even" set. The theory of fractals came up in the 1960es and so it is a new part of geometry which tries to describe unregular and fragmented forms or figures - like clouds, valleys or coastlines. This is where the classical Euklidean Geometry fails. There are fractal model which create picture looking like icebergs or plants. So fractals are a possible way to describe nature.