purpose of outer sheath in Foiled Twisted Pair network cable?
About the use of an outer, general shield over the individually shielded twisted pairs, it should enhance the electromagnetic interference of the whole cable. Remember that the insulator around the cable, because of it's non-conductivity, is prone to accumulate electrical charges. Using a shield layer directly beneath it helps dissipate these charges. You could say they would dissipate on the shielded twisted pairs but a constant layer of shield put directly under the insulator is better.

About screening, I assume you speak about braids (inter-meshed layer of small conductor wires instead of a plain foil). If so, the reason is mechanical. The use of braids enhance the flexibility of the shielding, in regard with that of an aluminum foil. As an analogy, it is (kind of) the same principle than using multistrand wires in an electrical circuit vs using a full wire. It bends more easily that way and cables subject to movements might be required to be braided instead of foiled, depending of the norm used (braids are more expensive than foils so they allow to use foil when it is ok).

Edit: As @horta mentions on it's answer, braids usually have a lower resistance (more conductive material or "area section" in them) than foils (thinner, less "area section"), which is better is better to dissipate electrical charges.