in short, a mesh that is animated has a Skin applied, which means it has bones applied to it, one or more.
Each vertex moves according to the bones, but for ex. if you move the bone for the arm, the leg must not move.
This means the vertices in the mesh for the arm are depending on the bone for the arm.
These vertices are "weighted" to that bone.
You can also apply an envelope to that bone, this means how far the influence of the bone reaches
So why are your textures so different, is that they are not handpainted, and they are not extually textures, but just some images on meshes (that's what I can could tell from the image you posted)