UV Mapping 101: Dang, Leatherface flattened out all that skin. Wrapping it around his head now requires unsightly seams!
How do you wrap a 2D image around a 3D object? It's a bit of a conundrum, and there's no perfect or easy way to do it (see Leatherface, above). It's more art than science, more ballet than ballistics, more Texas Chainsaw Massacre than . . . well, you get the picture. I've always been freaked out by the fact that there's no perfect way to translate the earth's surface to a 2D plane. Cartographers have been at it for ages. You either get distortion (Mercator's giant Greenland issue) or several discontinuous surfaces. In any event, you ALWAYS get a seam(s).
Aieee! Fair North America split in twain!!! The "orange slices" required to unwrap the globe using an "interrupted sinusoidal" projection.
Fools! Greenland will destroy you all!!! - The polar aggrandizement of the Mercator projection.
So. . . covering 3D surfaces with 2D imagery is an imperfect business fraught with peril, but that's the fun of it. Take lots of deep breaths and romantic walks in the park, and you'll be fine.