If you just consider the second part of my question, "Why a developer should not be interrupted while neck-deep in coding", that has been discussed a number of times by smart people. Heck, even the co-founder of SO, Joel Spolsky, wrote a blog post about "getting in the zone" and "being knocked out of the zone" and why it takes an average of 15 minutes to achieve productivity when participating in complex, software development related tasks. So I think the why has been established.

What I'm interested in is how to explain all that to somebody who doesn't know beans about Beans (khmm I mean software development). How to tell the wife, or the funny guy from accounting at the workplace, or the long time friend who pings you on Skype every 30 minutes with a "Wazzzzzzup?!", that all the interruptions have a much deeper impact on your work than the obvious 30 seconds they took from your time. Obviously you can't explain it by sentences like "I have to juggle a lot of variable names in my short term memory" unless you want to be the target of blank stares or friendly abuse.

I'd like to be able to explain all that to non-developers in a way that will make them clearly understand - without being offensive, elitist or too technical.

EDIT: Thanks to everyone for their great insights. I've accepted EpsilonVector's answer as his analogy was the closest one to my original needs. The "falling asleep" explanation is neither offensive nor technical, almost anyone can relate to it, and the consequences of getting disturbed while falling asleep or while being in the zone are very similar: you experience frustration and you "lose" 15-20 minutes of time.

Try the following analogies: 
First one:
"How long does it take for you to fall asleep?" "X minutes" "Now imagine that when you are close to falling asleep, someone walks in and interrupts you, how long will it take you to fall asleep now? Those few seconds you had left, or will you have to start again to 'sink back' to where you were?" "I'll have to start again" "Great. Same thing. Just like falling asleep, it takes me a while to 'sink' into focus mode, and it takes me a while to get back to it once I'm interrupted, except that I also forget half of what I was doing." 

Second one: 
"You know how when you're reading a book you 'sink into it'- after a while you don't even notice the words anymore, and you block out everything around yourself, and are totally immersed in the mental images you see." "Yes." "How long does it take for you to get there?" "About X minutes" "Now imagine that when you are that immersed in the book someone walks in and interrupts you, how long will it take you to get back to that? Will it happen immediately, or will you have to start again to 'sink back' to where you were?" "I'll have to start again" "Great. Same thing. Just like with reading, it takes me a while to 'sink' into focus mode, it's just as annoying when someone breaks me out of it, and it takes me just as long to get back to it once I'm interrupted, except that I also forget half of what I read." 
