A strange attractor is one that has the form of a fractal, or one that has "sensitive dependence to initial conditions". In other words, two rain drops might start out in more or less the same place, but their paths can diverge a lot over time.
Fractal is a word that started out as a short form for "fractional dimension".
The Mandelbrot set, Cantor set, and Sierpinski Triangle are among the most famous fractals.