How dangerous is a bare wire?
As pictured, the outer insulation jacket has cracked or split (because of cheapness on apple's part which they refuse to acknowledge and recall, but I digress), exposing a metal braided wire. This wire is a shield cable, used to protect the signal carried by the wire from interference, and prevent it from interfering with other devices. That shield braided wire surrounds another, thinner piece of insulation, which has the actual power and data wires inside.

The shield is often tied to the ground return wire of the cable, on one or both ends, and typically is safe to touch. The typical metal cased computer would be grounded in the same way, and these can be freely touched without harm. As the iPad is a low voltage DC device, and that crack appears on the lightning connector end, you would not be exposed to mains voltage.

That said, the cable has been compromised,  and continuing to use it as such is up to you. You should insulate the crack by some means, heat shrink tubing, electrical tape, plastic molding, etc, not just to prevent accidents, but to strengthen the cable at that point to prevent further damage. It is now a weak spot for the inner wires, a stress point where bending will have a greater impact.