From Destinypedia, the Destiny wiki
Story missions are activities in Destiny that can be played cooperatively in fireteams, with a maximum of 3 players. They often have ties to the main story arc of the game. These activities appear at various levels (numerical, relative to the player) and choosing a higher level (relative to said player) results in additional challenge by adding the Heroic modifier. Every day, a mission is chosen at random to be the Daily Heroic Story Mission that has another modifier and offers a higher reward.
Story missions are unlocked by advancing through Quests. Story missions can be replayed at any time, but without additional rewards received during Quests.
List of missions
List of appearances