TSV stands for "trainer shiny value." Basically, every Pokémon (and egg) has a shiny value, and if that value matches its trainer's shiny value, it comes out shiny.
The trick is that an egg's shiny value is assigned when the egg is obtained, but shininess isn't determined until it hatches. So if your egg has a shiny value of 42, you can trade it to someone with a TSV of 42, and it'll hatch shiny. --- Oooh, MM, he be tryin' you, dawg. He be tryin' you. Best mind you biiiiiiiz-ness. ~KMA *triple z snap* ~AluminumTicket
Every trainer in the game, when started, gets assigned a number: a hidden Trainer Shiny Value. Every egg and, in fact, every wild Pokemon encountered has a hidden Shiny Value number as well. When the trainer hatches a Pokemon egg or encounters a wild Pokemon whose Shiny Value matches their Trainer Shiny Value the resulting Pokemon is shiny, 100% of the time.
People are using a program called Instacheck in order to reveal these values and produce shiny Pokemon by trading their eggs to a hatcher with a matching Shiny Value.
That's pretty much it in a nutshell. --- Pokemon Y: 0318-7403-4577 | IGN: T.C. | Trainer Shiny Value: 2552 Safari: Ground | Pokemon: Camerupt, Wooper, Diggersby