One article I ran across defines it like this:
The lit color of a vertex is the sum of the material emission intensity, the product of the material ambient reflectance and the lighting model full-scene ambient intensity, and the contribution of each enabled light source.
Each light source contributes the sum of three terms: ambient, diffuse, and specular. The ambient light source contribution is the product of the material ambient reflectance and the light's ambient intensity. The diffuse light source contribution is the
product of the material diffuse reflectance, the light's diffuse intensity, and the dot product of the vertex's normal with the normalized vector from the vertex to the light source. The specular light source contribution is the product of the material specular
reflectance, the light's specular intensity, and the dot product of the normalized vertex-to-eye and vertex-to-light vectors, raised to the power of the shininess of the material.
All three light source contributions are attenuated equally based on the distance from the vertex to the light source and on light source direction, spread exponent, and spread cutoff angle. All dot products are replaced with 0 if they evaluate to a negative
value. Finally, the alpha component of the resulting lit color is set to the alpha value of the material diffuse reflectance.
If I understand it properly, there's a certain amount of global ambient. I light's ambient can allow for 0%, 100% or perhaps amplify the ambient within it's domain. The material ambient is how much of the resulting ambient is seen. 0% (Black)
and ambient has no effect, 100% (White) and global ambient is fully applied. I don't have access to Max or I'd try some tests to see how it handles things. As I said, I never liked the per-light ambient. It doesn't seem useful (realistic).
In the Torque engine they also have the ability to override certain lighting properties like adding a custom ambient value that's independent of lighting.