The reason for difference in skin colour is because near the equator the skin must be protected from too much ultraviolet (if your skin was too light you'd die of skin cancer), but further away dark skin blocks too much ultraviolet and you can't make enough vitamin D (so if your skin was too dark you'd get rickets etc.)
Other differences (facial features etc.) are probably party because of the environment (maybe a slender nose helps reduce heat loss) but more likely because of sexual selection, where people who look a certain way were considered more attractive in that culture and so were more likely to have more children.
it's worth mentioning that these differences emerge due to gradual, random mutation - the change isn't going to automatically occur in every isolated population that has migrated towards/away from the equator. These mutations are simply retained due to their beneficial, adaptive nature, which is what Darwin was referring to by the 'survival of the fittest' (note that anyone who develops a justification for eugenics from that has misinterpreted the idea). Those that don't develop them, on the other hand, will likely die out, or will be forced to migrate to other areas.
Complicated topics explained, simply.