What exactly is Shimano's Shadow Plus technology for rear derailleurs?
TL;DNR
A Shimano 'Shadow Plus' or SRAM Type 2 dérailleur (aka clutch dérailleur)  means you can change the chain tension by flicking a lever. 

For completeness - back in the late 2000's, Shimano introduced the 'Shadow' dérailleur (refer OP's link) which brings the deraileur in behind the cassette, providing it more protection from knocks and damage.  A short time (couple of years?) later they added the 'clutch' which in reality is nothing to do with Shadow, but Shadow was still new, and they still sold non-shadow dérailleurs in the lower spec ranges, so the needed to keep Shadow in the name of this new model. Even though/because all clutch dérailleurs were also Shadow, it made a lot of sense for marketing to call them 'Shadow Plus' rather than call them 'Plus'  

Unfortunately because of the close time frame between introduction, Some people mistakenly believe 'Shadow' means it has a clutch, as they never saw a 'Shadow' without the clutch. 

So what is Plus - As alluded to by @Batman's comment - The Plus means a clutch.  But what is a clutch


  Dictionary: noun: clutch; plural noun: clutches

1.
a tight grasp.
"she made a clutch at his body"
    a person's power or control, especially when regarded as inescapable.
    plural noun: someone's clutches
    "Tom had fallen into Amanda's clutches"
2.
a mechanism for connecting and disconnecting an engine and the transmission system in a vehicle, or the working parts of any machine.
"she let the clutch in and the car surged forward"
    the pedal operating the clutch in a vehicle.
3.
a group of eggs fertilized at the same time, laid in a single session and (in birds) incubated together.
4.
a slim, flat handbag



But the Shimano marketing term is none of the above. SRAM used a more generic term "Type 2" 

Going back even further than that (early/mid 1990's if memory serves me right, but might have been the 80's) Shimano came up with a 'new dérailleur' with a lighter spring and lowered chain tension. This was sold as having all sorts of advantages over the heavier springs - easy wheel changes, better drive train efficiency, probably making you more attractive to opposite sex was somewhere in there (it was the 1990's).  When it became apparent that MTB's were suffering because the spring was too light, its was going to be difficult to sell a "heavy spring" without Shimano getting egg on its face (as riders would become less attractive to the opposite sex). They developed the 'clutch' - a little lever that lets you have all the advantages of a light spring (easy wheel removal is the main claim to fame) and all the advantages of a heavy spring (less chain slap, better chain retention over rough ground etc).