It's basically the same reason why sunsets are red - scattering. Skin, muscles, and tendons are not completely opaque (absorptive), but you can't ordinarily see through them, either, because the light is scattered in all directions. Shorter wavelengths (blue and green) scatter more easily, meaning they go through more "bounces" trying to get through your hand and are much more likely to be ultimately absorbed. Red light is the least deflected by the scattering centers (inhomogeneities) in tissue and therefore the most likely to pass through. Infrared is scattered even less, which is why it is used for a lot of dermatological diagnostic tools.