What does special attack do on Pokemon mystery dungeon explorers of sky?

Answer 1

Attacks using your pokemon's teeth, claws, tails, wings, etc tend to be Physical Attacks, and these use your Attack stat.

Attacks that take the form of beams, flames, bolts of lightning, are Special Attacks, and these use your Sp. Attack stat.

Mystery Dungeon is a little more flexible than the main pokemon games. Feraligatr for example is a potent physical attacker, meaning it does more damage with a relatively weak Physical Attack, than a comparatively more powerful Special. The reason is, because Feraligatr's Attack is much higher than its Special Attack.

Mystery Dungeon pokemon don't tend to develop in quite the same way, but it's worth keeping in mind that if your pokemon has been affected with a status effect that lowers Attack, it might be better to switch to Special moves until you can cure the status effect, etc.

Answer 2

Special attack is another form of determining a pokemon's strength when using special attack moves. The special attack stat is what determines the overall strength of a special move such as Psychic the more special attack your pokemon has the stronger Psychic will be and so on.