A hook that hangs on (is supported by) nothing. Obviously an imaginary object, but a useful one.
Webster lists the word as coming into existence in 1927, but I don't know who coined it, or for what reason.
Also, a helicopter mounted with a steel line and hook, used to lift and transport heavy objects.
And also, a tall crane.
Or a skyhook can also be a surface to space elevator transportation system. (Click the link for a good description). Basically, if you get a long enough cable, centrifugal force will keep it up. Thus far these exist only in works of Science Fiction, but we're keeping our fingers crossed. These would be a very effective way of getting stuff into orbit.
And finally, in mining
engineering, "skyhooks" refers to the practice of driving bolts into overlying rock strata
as reinforcement for the mine
You might also be looking for the band, The Skyhooks