Figure 1: Direct and Indirect Illumination from a single directional light source. 
This post is part of the series “Finding Next-Gen“. Original version on 2015/11/08. Liveblogging, because opinions evolve over time.
Global illumination (GI) is a family of algorithms used in computer graphics that simulate how light interacts and transfers between objects in a scene. With its roots in the Light Transport Theory (the mathematics behind energy, how it transfers between various media, and leads to visibility), GI takes into account both the light that comes directly from a light source (direct lighting/illumination), as well as how this light is reflected by and onto other surfaces (indirect lighting/illumination).
As seen in Figure 1, global illumination greatly increases the visual quality of a scene by providing a rich, organic and physically convincing simulation of light. Rather than solely depending on a manual (human) process to achieve the desired look, the mathematics behind GI allow lighting artists to create visually convincing scenes without having to worry about how they can manually replicate the complexity behind effects such as light scattering, color bleeding, or other visuals that are difficult to represent artistically using only direct illumination.