Building, rigging, and animating characters is a lot of work. With all that work, many people overlook one of the most important tasks in creating a character—the textures. Textures play a very important part in the way a final image looks. Even the best model will look only average with poor texturing.
Texturing a character is very much a visual exercise. If the texture looks right, it usually is. There are other issues, such as getting the resolution of the texture maps correct, and making sure that the textures fit properly on the character.
There are two major ways to create textures: bitmaps and procedurals.
Most people use bitmaps to texture characters. The reasons are pretty straightforward: Textures allow artists to scan, photograph, or paint images. This speaks directly to the creative side of the artist, who simply wants to paint the character.
The downside to bitmaps is that they are tied to the resolution of the output medium as well as where the character is on the screen. The textures on a character created for television (640x480 pixels) will not scale up for a motion picture (2048x1170), for example. The larger the final rendered image is, the larger the bitmaps need to be.
If the character is standing full-screen, then the bitmaps will need to be at least the size of the output medium. If the camera gets closer, the bitmaps will need to be even larger. On some films, the bitmaps can be as large as 5K per image.