An attack is an action performed in the Battle Phase. To attack the player must have at least one monster in Attack Position, with exceptions being "Total Defense Shogun" and "Elemental HERO Rampart Blaster", who may attack while in Defense Position. Performing an attack means you enter the Battle Step. Attacking is one of the main ways to inflict damage to your opponent.
In the anime, when a player declares an attack, the monster literally attacks the attack target. In most cases the weaker monster will just stand still while the other one destroys it, sometimes it will try to fight back, but will obviously lose unless the player somehow makes it stronger. Some attacks are also given names.