Whenever cats get up after sitting or lying down, they stretch. Luxurious stretches, forward and backward. Why? Do they have super-contracting muscles that require excessive stretching? Do they get cramps? Is stretching a particularly fun time for cats?
Most animals stretch alot. It is good for you, feels good, and helps prevent muscle injuries.
The more perplexing question in my mind is why humans stretch so little.
That is why humans can’t catch mice; we aren’t limber enough. 
Cats are hunters of opportunity and so anytime they wake up from sleeping, they stretch so they are immediately ready to hunt. If you watch slow motion film of large cats running, you will see that they don’t just kick their legs forward to run, they also flex their backs alot and so they run with their legs but they also run with their backs. You gotta stretch it all if you want it all to work on a moment’s notice.
Humans find it cute. They kept cute animals as pets, and the behaviour was reinforced.
awwwwwww…
Anyone else read the thread title and assume the OP had a cat on the rack in her basement and…No? O.K.
Now that gave me a good snort.
But the factual answer is that cats stretch luxuriously all the time to show off their luxurious lives! “Off to work again human? Ahhh, I think that I’ll lie here in the sun, stretch, then go back to sleep. Bring me some nice treats when you come home. Ta ta, off with you now.” They get fiendish pleasure from this.
it is because they sleep so much…
I have no constructive information to add, but if some cat-stretching expert comes along…
Could it have something to do with the way they sleep? My cats (and many cats I’ve seen) often sleep curled up in a little bun. I’m not about to experiment with this myself, but I would think sleeping coiled up like that would necessitate all kinds of stretching. Heck, I do all kinds of stretching when I pry myself out of an airplane seat.
–Amy