Diffuse Interreflection is by far the most visually important global illumination lighting effect. Light bounces by default with Lightmass, and the BaseColor term of your material controls how much light (and what color) bounces in all directions. This effect is sometimes called Color Bleeding. Diffuse Interreflection is incoming light reflecting equally in all directions, which means that it is not affected by the viewing direction or position.
Here is a scene built by Lightmass with a single Directional Light and only direct lighting shown. The areas that are not directly visible to the light are black. This is the result without global illumination.
This is what the first diffuse global illumination bounce looks like. Notice the shadow behind the chair on the left, this is called an Indirect Shadow because it is the shadow of the indirect light. The brightness and color of the diffuse bounce depends on the incoming light and the diffuse term of the material that the light interacts with. Each bounce is darker than the previous, since some of the light gets absorbed by surfaces instead of being reflected. The pillar bases get more indirect light than other surfaces because they are closer to the areas in direct light.
This is the second diffuse bounce. The light has become much more attenuated and evenly distributed.
And here is the scene with four diffuse bounces combined. Simulating global illumination creates much more detailed and realistic lighting than manually placing fill lights. Indirect shadows in particular are not possible with fill lights.
Bounced lighting picks up the diffuse color of the underlying material, as you can see below. This is where the term Color Bleeding comes from. Color Bleeding is most noticeable with highly saturated colors. You can exaggerate the effect by raising DiffuseBoost on the Primitive, Material, or Level.