The main source of increased productivity from this is actually extremely simple to comprehend. If you are like most programmers or writers or even editors, or graphic designers.... etc. you will most likely have source material, or photos or some such open all at once. I have designed web pages and working on a single screen is really slow compared to working on multiple. It is a quantitative increase in amount of information to a flick of the eyes versus at a minimum one mouse click or alt+tab. The difference is startling!
Another issue that never was brought up in the article linked was the whole scrolling right and left problem. If you are a programmer or web designer or editor of some sort. You are bound to have at minimum 3-5 windows open at the same time. As a programmer probably a window with functions and one with the entire program on it (depending on the language) or multiple programs even. To work with that and keep it uncluttered think about it this way: Is it easier for you to have a 17 x 20 Inches desk space where you have to keep 4 documents you are working on hand writing as well as the 3 different resource materials open, or is it easier to have the standard 4-5 foot long and 2 foot wide desk space? That is the comparison for the non computer illiterate that will open their eyes to the idea of multiple screens. To get a screen that would be large enough to put what you can put on two computer screens side by side would cost about 1-2 thousand dollars (thats for a decent or higher quality 45-55 inch tv screen) where you can spend 200-400 dollars and have 2 22-24 inch screens that you can put just about as much on.
That is the difference because everyone thinks about alt+tab or the various other ways to quickly switch windows, but once again thats similar to having 4 documents on the small space along with research material. It is never as efficient as the multiple spaces or one massively larger space