Soft Reseting is basically a technique used to catch Stationary Pokemons in their shiny form. Most commonly used for Legendaries, Soft Reseting (SR, though not to be confused with Stealth Rock) helps a trainer get a desired shiny legenary by saving before they try to catcht he Pokemon. If it is not shiny, you reset back to the position you were by pressing Select + Start + L +R (for DS systems) or Select + Start + A +B (for Gameboy games), thus giving you a chance to get it in it's shiny form. Beware that to get a shiny is very time-consuming, though worth it.
**EDIT: note that this cannot be done with event Pokemons, or shiny-locked Pokemons.