Quest
Also said as Mission, Side quest, Task
A unit of story with a goal, some obstacle and an outcome, tracked by the game. A side quest is one the main plot does not require.
Quests are how a large game hands out story in pieces the player can pick up and put down. A good side quest has its own small arc and leaves a mark on the world, and a poor one is a shopping list.
Say it
“Every side quest needs to change one thing in the world: a shop opens, a road is safer, or someone is gone. If it changes nothing, cut it.”
Where you’ve seen it
Mass Effect 2's loyalty missions are optional side quests, one for each crew member. Whether you did them helps decide who survives the final mission, so skipping the side stories has a real cost.
Not to be confused with objective
An objective is one step: go here, kill that. A quest is the whole story those steps belong to.