A kitty-cat dance is any series of pointless, silly or superfluous steps that must be performed to satisfy people that adequate effort has been expended. It can also refer to needlessly tedious steps taken to accomplish an otherwise simple task.
The requirement to get three signatures from three different offices, all of which require appointments on separate days, just to get a paycheck problem solved is a kitty-cat dance. So is stepping through six pages of provably worthless, irrelevant network troubleshooting, when you already know that the problem is a toasted router.
Kitty-cat dances are most commonly associated with the government, either federal, state or local, but are hardly unknown in business, either. Just read Dilbert some time!
The term is derived from an incredibly goofy video of a dancing kitty, which constituted a minor internet meme for a while.