Many of the tutorials that I have come across have been very thorough in explaining how we use UVs and UV Mapping when texturing a model, but one thing nearly all of them have neglected to explain is why.
When I begin my tutorial, one issue that I would want to address is why UV Mapping is the method for applying texturing to Polygon models, that is universally accepted by industry, and not any other method.
In looking for a decent tutorial on UV mapping, I came across the Gnomon Workshop lectures on UV Mapping. Unfortunately, I cannot upload the video clip, but the lecturer explains that UV co-ordinates are components that allow you to manipulate the positioning of a texture on a Polygon model. This is largely because Maya will not be able to figure out how you want a texture to fit around an object by itself. UVs can be used to control how distorted or how clear a texture looks on your model.
UV co-ordinates are essentially components, just like vertices, edges or faces; but they are specifically used to manipulate the texturing rather than the corner or edge of a Polygon shape. Moving each individual UV to get the texturing on a model perfect is very time consuming and this is why we produce UV maps.
UV Mapping is a method of laying out all of these UVs in a meaningful arrangement. UV maps enable the you to see all of the UVs laid out in 2D against the texture, so that you can see what changes need to be made to the UVs in order for the texture to fit the model.
When I start recording my tutorial, I will begin by establishing that UVs are components of a Polygon model that allow the user to adjust the positioning of texturing on that model (much like vertices adjust the positioning of a specific point on the geometry of a model) and that UV Mapping is done to arrange these UVs into a meaningful form.