Here's how the move works. Since Psyshock is a special attacking move, the Pokemon using the move's special attack stat can control the move's damage. However, the defending Pokemon's defense stat comes into play instead of special defense.
Example: Your special-attacking Pokemon uses Psychic against say, a Blissey. Blissey's special defense stat is really high so it tanks the damage. However, if you use Psyshock, then it would do more damage because Blissey's defense is lower.
Hope that wasn't too confusing! :)