When rendering, Maya takes into account all of the various objects and scene attributes, and performs mathematical calculations to produce the final image or image sequence. Once you render a sequence of images, you can then play them back in sequence, producing an animation.
In Maya, rendering can be accomplished using software (Maya Software Renderer, mental ray® for Maya® Renderer, or the Maya® Vector Renderer) or hardware rendering methods. Each type has its distinct advantages. Which renderer you decide to use will be determined by your image requirements (that is, the look you require) and time constraints.
Software rendering generally allows you to create more precise results but can take longer to produce each frame or image. The Maya software render type uses a process for scene illumination that directly illuminates objects in the scene or simulates illumination by reflecting neighboring objects in the scene or via texture mapping the effect on the object.
The mental ray® for Maya® software render type additionally provides a feature called Global Illumination: a process that simulates the effect of indirectly illuminating objects that are not receiving direct illumination. It can also simulate light effects known as caustics. Hardware rendering is generally faster but is less capable of producing detailed results. In addition, some visual effects can only be produced via one method; at times, a combination of more than one type of rendering method may be required.
Rendering usually requires several iterations to achieve the final image that meets your requirements. The key is to strike the balance between producing the image that meets your requirements and producing it in the time required. This is particularly important if you are using Maya in a production setting.