The definition is mathematical and a bit sophisticated for non-specialists, but descriptions are fairly easy to come by. They have an infinite amount of detail, and this detail is often composed of small copies of the overall item. Fractals, however, cannot. They are generally defined recursively, that is, start with something, apply a rule to it, apply the rule to the result, and continue until something happens. Anyway, . .
Clouds are fractals.
Shorelines are fractals. Mountain ranges are fractals. Mathematical formulae exist which emulate these natural shapes and draw them on the computer in the form of pictures. Other irregular shapes not known in nature may also occur. Fractals are purty.