Okay, I'll take a crack at it. If I commit any howlers, please note it's been 17 years since I've taken any college-level physics /ubbthreads/images/graemlins/smile.gif
Okay, I do think it's possible to explain this to a layman who has at least some basic physics knowledge. Here's how I'd start explaining it:
Electrons form a cloud around an atom. The electrons are in "orbits", and those orbits correspond to different energy levels. An electron with a relatively higher energy level is said to be in a higher-energy orbit than an electron with a lower energy level. When an electron in a high-energy orbit drops down to a lower-energy orbit, it has to shed the extra energy, and it does so by releasing a photon (light). What an LED does is create the conditions where high-energy electrons drop to low-energy electrons, and shed the extra energy as light.
That's probably enough to make most people happy, but what if they ask for more detail (perhaps, like me, they've had physics 101! /ubbthreads/images/graemlins/smile.gif Then you can launch into the more detailed explanation:
First, you take a material that has some electrons missing from it. Don't worry about how we create a material that has missing electrons, just trust me, they're missing. We call the spots where the electrons should be, but are missing, "holes". Since this material has missing electrons, it is positively charged.
Then we take a material that has extra electrons in it (see previous note on how we created this material). Since this material has extra electrons, it's negatively charged.
As a side note, the two materials I just described above are based on the exact same stuff, but different types of impurities are added (this process is called "doping") to get the material to end up with extra electrons or holes.
Okay, now, we take the two materials above and we put them together. When we apply a voltage in the correct direction across this material, the extra electrons from the negatively-charged side move towards the junction where the materials meet, and the holes from the positively-charged side also move towards the juncture. At the juncture, the holes and electrons meet, the electrons fall into the holes (recall a "hole" is a spot where an electron is missing). When an electron falls into a hole, it drops to a lower energy level, and as we know, gives off the extra energy as a photon.
So, now the question is: if electrons are moving one way (towards the center of the material), and holes are moving the other (also towards the center, but from the other side), how does a current get generated? It takes a bit of thought, but if you think about it, electrons moving one way is exactly the same thing as holes moving the other way. Think about a bubble rising to the surface of a glass of water. You can think about the bubble (the hole) moving upwards through the liquid. Or, you can think about the bubble being stationary, but the liquid flowing downwards around the bubble. You can model the process either way, but the results are the same: the hole ends up at the top, the liquid at the bottom.
That's exactly what we're seeing with the LED. If you want to think of current as "electrons moving from left to right", then what you have is (say) electrons moving from the leftmost lower-voltage direction to the right towards the LED's juncture, and you have holes moving from the higher-voltage side moving from the rightmost higher-voltage direction towards the LED's juncture. But since we already said that "holes moving from right to left" means exactly the same thing as "electrons moving from left to right", that's how electrons get all the way around the circuit.
Joe