Attack and Special Attack affect the power of physical and special moves, respectively.
A Pokémon like Gardevoir, with awesome Sp. Attack but cruddy Attack, will use the superior stat to it's advantage and use special-based moves like Psychic. A Pokémon like Scizor, with high Attack but awful Sp. Attack, will use its superior Attack stat to boost the power of physical-based moves like Bullet Punch.
The reason people want certain Pokémon to be trained in Attack or Special Attack is so that they can capitalize on that Pokémon's strongest offensive stat. The result is that you don't see Special Gyarados or Physical Sylveon.
People put EVs into the strongest stat to make it even stronger. It's pointless to put 252 SpA EVs on a Heracross with all physical moves, so the smart and logical thing to do is put them in Atk to make dem Megahorns hit as hard as possible.