Attempting to decisively strike at one of an opponent's bases. It is different from harassment in that it is designed to destroy enemies units and enemy bases or control territory, rather then slow the enemy's overall econ or tech progression.
Production buildings are key elements of an attack. As games progress, players who decide it's time to attack will first make large numbers of production buildings (like factories, gateways, or hatcheries), up to 8-10 or more. This allows them to mass enough units to overwhelm the opponent, as well as quickly provide large numbers of reinforcements. Ideally, the opponent will not realize a player is building production buildings, and so will be at a significant unit disadvantage due to their fewer production buildings.
Many times, a player will opt to slowly push rather than to charge across the map, to secure territory or bait a weaker force into a counterattack. Even when charging, it is critical to stop and gather units just before the attack begins. Units which stream in a straight line into an attack significantly reduce their firepower and maneuverability, exposing their flank.