Soft Resetting means pressing certain buttons to reload the game from the Startup screen. Hard Resetting is, as you said just turning it on and off.
This practice is widely considered useful, as rebooting the game will modify hidden data values. The values that determine the shininess of an in-game event Pokémon is of particular interest here, as are the Pokémon's IVs and Natures. Soft resetting eliminates the need to constantly turn off (and on) the game when attempting to get a Pokémon with these specific qualities. Although time-consuming, it is a widely practiced method to get a desired Pokémon.
Button combinations for Soft resetting:
GB/GBC/GBA games: Press and hold A, B, Start, and Select.
XD: Gale of Darkness: Press and hold B, X, and Start.
DS games: Press and hold L, R, Start, and Select.