"Quest line" refers to a series of tasks or objectives that a character or player needs to complete in a game or story in order to progress or achieve a goal. Full definition
You just follow the main quest line in your journal or do side quests. (n4g.com)
So far I've completed the main story quests for one of the seven character classes and have done the first third of the main quest line for a second character. (andymerrill.com)
Players can set off to adventure through five new quest lines, featuring new characters with their own motivations and agendas. (gamespace.com)