A catwalk is originally a nautical term. It indicated an elevated walkway on a ship, one which required caution to properly traverse. The user was obliged to walk 'like a cat' - very carefully and sure-footedly - in order to safely pass along it. Modern shipbuilding refers to 'catwalks' as enclosed or covered elevated walkways - used either for bridge access or, on modern ships with large amounts of equipment on deck, to carry their users over the cluttered deck area (Liberty Ship terms). Another nautical reference indicates that long, narrow 'finger piers' are also referred to as catwalks.
The term carried over to refer to similarly constructed passageways in various situations. In a theater, a 'catwalk' is an elevated walkway behind and above the stage, where caution and balance are essential. These catwalks, being (usually) indoors, are not covered or enclosed, and in modern everyday parlance catwalks have come to indicate these sort of raised platforms. Typically, they are metal, elevated a significant (dangerous) distance above the floor or ground, and usually have handrails or guide ropes. They are usually quite narrow, however.
Eventually, the use of catwalk in theater migrated to the fashion industry. The practice of erecting a raised walkway for models to parade on during fashion shows appropriated the term, since what they were walking on was a raised walkway, even if not railed or (usually) dangerously high. As a result, 'catwalk' now also refers to both the platform used by exhibiting models, and the activity or genre of clothing exhibition on live models.