It is a figure in the complex plane that illustrates whether the "equation" (more like programming language expression) z = z² + c goes to infinity or not. z=c is a complex number that you start with on each pixel you render and in every step you change z according to the formula while c stays constant. You render the pixel black if you reach infinity (in practice a treshold). You can color the surroundings based on how fast they approach infinity or assign them a height on the Z axis, creating a 3D figure.

The Mandelbulb is different as it does not use Cartesian coordinates.