DM: "The stranger in the tavern tells you of a ruin full of treasures to the north of town. What do you do?"
Players: "We go south!"
One of the developments in modern MMORPGs was the idea that the player should always be on a quest, or several, so he would never be lost for ideas on where to go next. Dungeons & Dragons 4th edition introduced that idea into D&D rules, but most of the official adventures I've seem don't actually use the concept. That is probably because those adventures are very linear already, and if you have a dungeon full of monsters you don't really need a quest to tell players what to do.
DM: "You found the sword Excalibur that King Arthur asked you to retrieve. He is waiting for you in Camelot, north of here. What do you do?"
Players: "We go south!"
A completely scripted and linear D&D adventure is a bad adventure. Much of the interest of pen & paper roleplaying is that the story is not completely predetermined, but evolves from the interaction between the players and the dungeon master. If the players come up with a great solution on how to infiltrate the keep instead of attacking it, great! But of course that leaves the risk of the players derailing whatever the dungeon master has prepared. And quests are a great way for the DM to let the players know where they are supposed to go, without actually forcing them.
Most likely your game world is full of interesting places, monsters, and treasures. Thus the mere existence of a dungeon full of treasures isn't motivation enough for the players to go there. Of course you can railroad the players to end up at the dungeon entrance regardless of whether they go north or south. But your players probably won't appreciate. Thus it is better to not only deliver them some story hook of why they should go to that dungeon and retrieve some item, but at the same time give them a piece of paper with a big heading: QUEST, a short description of what they should do, and an xp reward. Formulate item retrieval quests as "bring back" rather than "find", and the players might actually turn in the item they were supposed to look for instead of just keeping it.
Not all quests have to be solved. Some might even end up being impossible to finish, or two quests might contradict each other. Or the players might decide that even with a quest reward they aren't interested in that particular story line. But in general a quest gives both a clear enough signal, and a good motivation to players to not completely mess up whatever the DM has prepared. If your players constantly refuse all your stories and quests, it is probably time for "rock falls, everyone dies" anyway.
One other reason I like quests for is that they provide a convenient game mechanic for giving xp for non-combat activities. Next play session the characters in my group will finish the level 0 adventure, and build their level 1 characters. So I'm in the process of writing an adventure for level 1 for them, using a mix of pre-made adventures and own ideas. And unlike the official adventures I don't want them to be in combat all the time, but have a 50:50 mix of combat and non-combat encounters. Quests that give xp for let's say solving a murder mystery put the roleplaying encounters on the same reward level as the combat encounters, so players don't just simply go for combat all the time because it gives the best rewards. In the part of the adventure I've written up to now, which should get the players from level 1 to level 2, half of the xp are from combat, and the other half from quests, one major and two minor ones. That is more than the xp for quests foreseen in the Dungeon Masters Guide, but according to the DMG a minor quest gives less xp than a minor combat, and a major quest less xp than a major combat, and that is not how I want to run my campaign.