Quest Completion
"Quest Completion" refers to how the game officially recognizes you have completed a quest, which is not always the same from quest to quest.
Sometimes you go back and have ending dialogue with the same NPC who gave you the quest, but other times the quest is completed by killing all of the hostiles in the quest location. Watch for a quest completion message in your text box, which is an obvious indication you've completed the task(s) in the quest and you now need to do something next. However, not all quests have such a message.
In questlines, which are multiple quests connected by a story, a completion message will usually indicate how to move on to the next chapter of the story/mission. Blood-Soaked Heroes is a good example; as you go places and complete tasks, you get messages in your HUD's text box which help direct you along the way. The quest also registers in your Pip-Boy, and gets updated as you move through the chapters of the story, so even if you miss the text message, you can remind yourself what's next by referring to the quest in your Pip-Boy.
In the Gun Runners Caravan Package quest, you do not get a text message when you've killed all of the hostiles in the cave - because this was not your job, nor do you get a text message once you've obtained the objective item - because you still need to bring it to Marshal. You get the item, and likely have to kill some of the mutants in the cave to get it, and return to Marshal to give the Metal Case to him, BUT...in this case quest completion is accomplished by then speaking with [Ralph]] to choose your reward - like Marshal tells you via dialog, chat-log has it too and it is in your Pip-Boy as well. This is a repeatable quest, on a timer. The timer does not reset by turning in the Metal Case to Marshal. Instead, it resets once you've chosen a reward from Ralph. Many players have turned in the Metal Case and expected the quest to be completed, and the timer to reset, only to find out the next day they cannot get the quest again. Asking around, helpful players might point out they need to go back to Gun Runners and speak with Ralph.
In a Junktown Zombie Invasion, you have a 1-hour window to kill all zombies and return to Lee.
NOTE: After timing out without completion, some quests just reset, some go back to an earlier part of their questline, and some just fail.