Hopefully this will help make setting your Smoke Parameters a little easier.
Minimum Density is for instance if you have 10.0 values of smoke (example: you generate smoke with a simple source at a set value of 10.0) in a voxel, if your Min Density setting is at 5.0, the smoke will only begin to dissipate when the voxel contains 5.0 or less values of smoke.
This density value is constantly changing because of forces that are imposed on the grid like gravity/buoyancy/temperature/turbulence/spacewarps/ect. So it there were absolutely no forces to move the smoke around, the smoke in the 10.0 value voxel the smoke would never ever dissipate.
The Dissipation Strength Value is the easiest one to understand, it is simply how fast the smoke is going to dissipate once the Minimum Density value is reached. So going to the above example setting of 10.0 values of smoke in the voxel and a Dissipation setting of 99.999 if the smoke density in the voxel never gets to 5.0 it will never dissipate. BUT as soon as the smoke density in the voxel goes below 5.0 the smoke will immediately dissipate.
Diffusion simply diffuses the voxel much like adding a blur to a pixel in Photoshop. That is the only way I now how to explain it. The blur has the most density in the center and has a falloff to zero at the outer edges. So adding Diffusion takes that value of 10.0 and spreads it out (according to whatever algorithm it uses). Also note when you use diffusion it is constant, so the original voxel that contained 10.0 values of smoke is now spreading to neighboring voxels populating them with smoke, which are then being diffused again, and spreading to the neighboring voxels and so on.
Here is a little illustration to help: