Rendering is the process of taking what you have created in your scene (the models, the materials, the lighting and the animation), and creating actual imagery from that scene data. There are many different forms of rendering, but the basic process in all its forms is very similar. We start with the camera’s viewpoint, and then determine what needs to be a part of the image from that point of view at that particular time. In some cases, we may not be able to see everything through the camera that will contribute to the image—this is particularly true for reflections and lights, as their sources are often out of view at times throughout the animation.
Then, we walk through the database of the scene, and follow the instructions from the scene that inform us about what the final image should contain. This information is then sorted, applied, and interpreted as necessary. Once we have all of those basic contributors, we then process them to the level of quality needed to fulfill the requirements of the scene. And, once everything is properly accounted for and processed, we convert all of that information into a picture or movie.
Of course, there are many specialized mathematical routines involved (some that might make your ears bleed), and there are some hoops that need to be gone through (especially in the physical renderer when computing things like depth of field, and 3D motion blur), but in the end, the results are worth it.