The word "fractal" is short for fractional dimension. It's a geometric pattern that repeats itself at every smaller dimension to create countless number of replicas of the same pattern. This is done by adding a certain transformation to the original object. This iterating process is infinite so the complexity increases with every smaller dimension. However, not all iterations create fractals. For example, if you have a line and you take away part of it and continue that process over and over again, soon it will become a point and it's no longer a line. So basically fractals are any sort of curve or surface, and they"re free of scale. Fractals are referred to as self-similarity, which means that if any portion of the curve were to be blown up to actual size, it would be impossible to tell it apart from the whole curve. Fractional dimension provides a way to measure how jagged fractal curves are. Lines have a dimension of one, surfaces a dimension of two, and solids have a dimension of three. Roughness adds an increase in dimension. A rough curve has a dimension between one and two, and a rough surface has a dimension between two and three. The dimension of a fractal curve is a digit that makes up the way in which the measured length between given points enhance as the scale reduces. In Sierpinski's triangle, you start out with a two dimensional triangle. Then you take away from the triangle, a smaller triangle from the middle of the inside. You do this an endless number of times to get the Sierpinski's triangle an infinite number of times. Because you are taking away from the triangle, you are reducing the dimension. So you started at two and decreased it, but it will never reach one because it's nowhere near looking even close to a line.
The theory fractals was created by a French mathematician by the name of Mandelbrot. He was frequently called The Father of Fractals. He proposed his idea of fractals as a way to deal with the difficulties of the scale which caused many problems.