None: None leaves it as soft particles.
Lambert: Lambert make the volumetrics colour and luminosity changed based on where you're looking at it and where the light is hitting it. Basically the same as any other 3d shaded surface.
Phong: Phong is exactly the same except not only can light hit the surface and illuminate it, but it can make edges shine ect. just like with the phong shader within the material editor.
Ambient: Ambient controls the basic illumination and colour of each volumetric particle. If the scene you're in is a red enviroment you may want to tint your particles slightly red based upon this. This will allow you to do it very easily. It's exactly the same as the ambient in the enviroment panel.
Specular: This controls the colour of the gloss on the phong volumetric surface.
Shape/Noise: These are used for the normals, if you use shape then it'll use the bounding box shape (sphere, cylinder, box ect.) of the volumetrics to calc the normals, wheras shape does it based on the noise routine.
Shape influence: For the above, it gives a blending value basically allowing you to mix between the two.
Shinyness: How sharp the gloss is on a phong surface
Shin. Strength: How much gloss is applied.
Use: Turns reflections on or off
Strength: Allows you to give a reflection strength value, controlling how much reflection you want on the surface.
Reflect enviroment: This allows you to use an enviroment map on the volumetrics as a reflection map.
MtlID: This allows you to use material ID #'s on the surface of the volumetrics, this means you can use this info in video post to apply effects to the material ID #'s.
Scattering: Scattering controls the light scattering, working out how light is effected within the volumetric particle.
Isotropic is the default light scattering algorythm, it's fast and pretty much what you want to use all the time. These are calculated based on the lights strength, distance and the cameras angle, essentially like how falloff works.
HGS and Rayleigh are slower but sometimes better for illuminating the insides of volumetrics. You have Rayleigh, HGS and Isotropic.