Just a note, Feynman was very bad at explaining things to uneducated people. He was famous for his insights and ability to explain things to other professionals, but his lectures were very badly received by the students. So I'd take that statement with a grain of salt, as Feynman obviously have way better understanding than an average lecturer.
And that's how I explained the cloud to my grandma: the company buys big daddy servers which make baby computers that the company sells for profit. She was so happy she finally understood what my job was at the time.
When I read this gestation/birth analogy, it makes it seem to me like a large piece of hardware assembles and ejects a small piece of hardware. I assume in-person there was more detail or different imagery?
How about: instead of keeping photos in a shoebox in your cupboard at home, you can keep them in a container at a company's storage place. But people want their own box, so the company divide their container box up into pigeon-holes and fit all the shoeboxes in to the spaces in it. If you want to look at the pictures you can go and view them, you only have access to your own shoebox though.
Shoebox is logical computer, cupboard is computer, container is a distant "big" computer (server), pigeon hole is a virtual server.
Now you might have a few boxes of photos at different companies -- the cloud is being able to see/use all those photos at the same time from anywhere in the World.
[Perhaps too close to storage model vs processing model of cloud?]