Hybrid fractals occur when you alternate between fractal formulas during the inside iteration loop of generating a fractal. The idea came from posts on the old Fractal Forums site.
For example, rather than the usual Mandelbrot Fractal iteration, you can modify the inside loop to alternate between the Mandelbrot, then the Burning Ship, then the Mandelbrot, and the Mandelbrot again. You then repeat the sequence for as many iterations as that pixel needs.
This gives a result like the following
I have also used the same hybrid technique for 3D Mandelbulb Fractals as shown here.