Destroyed as a Result of Battle specifically refers to a monster getting Destroyed when attacked. Generally, when a monster has lower or equal ATK points while in Attack Position when it Battles with another monster, that card or both cards are destroyed, respectively. When a monster is in Defense Position and a monster attacks it with higher ATK than the monster's DEF, it is Destroyed as a Result of Battle. The monster is determined Destroyed as a Result of Battle during the Damage Step.
Many effect requirements can be fulfilled when a monster is Destroyed this way, an example being "Skyscraper 2 - Hero City".
If a monster Destroys its opposing monster during Battle with an effect, the card is not Destroyed as a Result of Battle. Examples are "Mystic Swordsman LV2", "Mystic Swordsman LV4", "Mystic Swordsman LV6" , "Drillroid" and "Ninja Grandmaster Sasuke".