Attack is a value that only presented on weapons. The attack value reflects the damage that is dealt to an opponent's battle car. It's measured in DPS, or damage per second. This means that a rocket with 200 attack value will deal 200 damage every second (however, it usually ends up being slightly over a second because of the projectile's travel time).
Slow-firing weapons like lasers will do more damage than their attack value. For example, a laser with 400 attack value will do 1000 damage to an opponent's battle car for every shot. This is because a laser takes 2.5 seconds to charge, therefore multiplying the attack value by 2.5.
Attack is important as it changes your possibilities of defeating opponents. Make sure you have a high attack value so that you can destroy opponent's car before his/her machine destroys yours.
Note that a car with high attack value does not always win. Play it smart.
You can fuse items with weapons to boost their attack value. Keep in mind that only a fuse that levels up the part will change its attack value.