they're basically the same thing except that skill makes you think of something learned, something you worked hard to be good at, whereas ability makes you think more of a natural talent. also, skill makes you think a little bit more about mental tasks like being smart, while ability is almost more physical, like sports.
His ability to run is astounding.
NOT: His skill of running is astounding.
He is very skilled at math.
His has great ability in math.