Gary runs a popular online shop that has just recently begun accepting Vertcoin. Everything is running great and all, but Gary is starting to feel that perhaps its a bit too open for his comfort. His competitors are able to see all of his sales as they happen, and well - Gary doesn't think that's right.
Vertcoin has recently introduced something called a "Stealth Address". With a stealth address, Gary can hide his sales from his competitors, and other nosey folk, and conduct his business operations in private. So Gary takes down his old Vertcoin address from his site, and replaces it with a shiny new Stealth Address.
Well, its not all that complicated. Gary puts his stealth address up on his website in public. Customers then all pay to this stealth address - just like his old vertcoin address. But then the magic happens behind the scenes.
This stealth address automatically creates a unique vertcoin address for each of his customer's transactions, making every customer transaction go to a different location - no more competitors snooping, or nosey customers! But that's not all... the other magic part is that, because Gary keeps the special "private stealth address key" - all of these new addresses, and all future ones - are instantly accessible via his Vertcoin wallet, as if they were all paid into the one account.
From there, Gary can conduct his normal business activity. Safe in the knowledge that his business is now private from the rest of the nosey world.