I know some math. Whenever I come across the word fractals, I see cool colourful pictures. So I googled it and can't understand a word about it in Wikipedia. Can anyone explain me what fractals are in a basic yet clear way?
Fractals are self similar structures with minor changes to the original. The best example is a tree. Say you have the root of a tree, and copy it, but reduce the length by 75% and rotate it 25 degress or something like this. then place it somewhere on the trunk. now you have two branches, you do the same to the second branch so that you get a third branch. Then you repeat this process all over such that you form a tree.
So best way to put it is that if you have some rules, you make copies to the object and change it so that you get some kind of large tree structure with branches that look similar to the original when you zoom in.
A great resource for this would be a course at the University of Waterloo by E. R. Vrscay called "Chaos and Fractals". His lecture notes are available free online here. Although a bit more advanced than elementary calculus, his course is self contained and provides excellent explanations of the more advanced topics you might not be familiar with.
Furthermore, this Numberphile video on the The Mandelbrot Set could be particularly enlightening.