Global Illumination is the collective name for a number of rendering algorithms that in at least some respect take the entire scene into consideration when doing lighting computations. There are also local illumination methods. Aqsis 1.0 is strictly a local illumination renderer, but global illumination effects can be simulated with very good results.
In a real scene, not only the light sources emit light, but objects that are illuminated reflect a significant amount of light back into the scene, and that secondary light can in turn illuminate nearby objects. This can make some objects appear to take on a tint of the color of nearby objects, an effect known as color bleeding, and light also reaches parts of the scene that have no direct path to any light source. A very crude but still quite useful way of simulating at least some of this spreading of light is to define an ambient light source, which illuminates all surfaces in the scene regardless of their position or orientation.
Shiny objects reflect the scene and each other, not just light sources. This can be simulated by reflection maps.
Ordinary shadows are another effect that require the consideration of more than the object that is being shaded at the moment. Global illumination models generate correct shadows as a side effect, while a renderer that does not use a global illumination model needs to simulate shadows by generating shadow maps in a pre-processing step before the final rendering.
In most scenes, the effects from interactions between objects are pronounced, and not simulating them will often yield a flat and unrealistic look in a CG image.