What is it?

As I understand it, Max Quadtree Depth is a mathematical process in Raytrace shadows for Standard lights that defines the subdivision of the search pattern of edges of objects in the scene.  The shadows themselves are defined by shooting rays from the viewer, to the objects, to the light source and the detail of the shadow is dependent on how many rays are fired.  However, I have yet to see a situation where adjusting the Max Quadtree Depth has affected the quality of the shadows.

Where is it?

If you select a Standard light with Raytrace shadows and go to the Modify panel you'll find Max Quadtree Depth is in the Ray Traced Shadows Params rollout and is set to 7 by default.  I'm not sure why this is the default setting because, in my experience, it's never been the optimum setting.  The minimum value is 1 and the maximum value is 10 and I haven't seen a situation where you would drop lower than the default 7.

So what do I do?

To find the “ sweet spot ” you must render this scene with 8, 9, and 10 to find the optimum setting for your particular scene.  I've heard people say that 10 is always the correct number, but I haven't found that to be true at all, so I encourage you to do a complete rendering with all three settings to make a comparison.

There are many variables that can affect the results; number of objects in the scene, relative size differences between the largest and smallest object, and distance of lights from the surface, just mention a few so it pays to experiment.

If you are using the Daylight system which, defaults to Adv.  Raytrace Shadows, the scene will always render faster than the default Raytrace shadows.  But it's still worth trying Raytrace shadows with the three settings as I've seen that renderings have often been noticeably faster than the Adv.  Raytrace Shadows.

While we're on the subject...

While this is not related to the Max Quadtree Depth, it is important for getting clean shadows.  If the edges of your shadows have jagged edges and no amount of adjusting of light parameters will seem to correct it then try setting the Super Sampling on in the Material Editor for the material receiving the shadow.  Be careful, however, because Super Sampling can make your rendering slow.