Jump In One's Skin Meaning

(idiomatic) To start with fright.

Example: 1883, Robert Louis Stevenson, Treasure Island, ch. 4:
  The neighborhood, to our ears, seemed haunted by approaching footsteps; and what between the dead body of the captain on the parlor floor, and the thought of that detestable blind beggar hovering near at hand, and ready to return, there were moments when, as the saying goes, I jumped in my skin for terror.