You can only do so much with 3D meshes, in fact to get nice looking mesh, would take quite a bit of polygon detail, which burns up a lot of processing power and for such things as computer games, would be too slow to draw on the screen in real time. Also you'd need to colour the mesh some how. You could just have flesh coloured mesh for skin, brown coloured mesh for hair or blue for the eyes. How about the pupils?, they're black, how about hair detail? more mesh??. Hey come on this is getting pretty heavy!
This is where applying a texture map (picture) to the mesh can save a lot of mesh geometry and provide, not only colour, but fine details, shadows and highlights as well, giving a high quality look using only a small amount of resources.
Below is a full body single mesh character model with a poly count (number of triangular faces) of 956 . This type of low poly model is ideal for computer games, but as it is, has very little detail.
A close up of this model shows that to get the low poly count, mesh detail such as fingers, eyes and mouth are missing. There is only the basic mesh necessary to provide an entity in 3D Space.
The quality appearance of this model will be provided by the texture map. The 3D mesh is merely the canvas, the texturing is the finished artwork.