If you will, picture the player: “Asking the cleric to draw the light as far back from the top as I can, I climb down the rope to the bottom of the chimney; what can I see with my infravision?”
“About forty feet down, there’s a metal plate set across the chimney. About ten feet below that, you can detect a swirling mass of color that you’re guessing is probably water.”
“I try to move the plate. Can I lift it?”
“Roll a d6.”
The situation I’ve descibed is typical. I’d like to point out, however, that I have not told the player specifically what they are rolling the d6 for. It might be to see if they can move the plate, and it might be surprise or initiative, since something could attack them. One way or another, I am very deliberate about keeping the player in the dark until I know what the die roll has told me. That way, if it is an attack, I can inform the player simultaneously that he is surprised, or not surprised, and that the alligator has leapt up to take off a piece of the character's foot.
I have been to many games where the dialogue between player and DM is all very technical ... where the DM describes the monster according to its type, species and even it's level or character class: "You see an ogre magi cleric master of the fifth rank" ... whereas I'm likely to say that you see an ogre with a sword (or possibly not; why couldn't an ogre magi carry a club?). I don't think it does any good to tell the players up front that the mage is casting a cause serious wounds spell until the actual spell is applied to the character. It is enough to know that the ogre has cast a spell, and that now the ogre has entered combat. I won't even say, "The ogre has cast the spell and now tries to touch you." That's too much information.
Half the fun of being a DM is keeping the players woefully in the dark. Sometimes, yes, it's obvious what they're rolling for. If they are on the edge of a cliff, and they've just been hit by a club, I will tell them to make a "dex" check ... they might as well know at that point that if they fail they're going to fall. But if they're crossing a courtyard, and I want to see if they notice that the statue in the center has just moved, I don't tell them that they're making a wisdom check (the roll I use for perception) ... I just say, roll a d20. I don't want them to know why. Particularly if they've failed. Then it is just hanging out there - the question, "What was that for?" might never actually get answered.
I think this bothers some DMs. I think that they are deeply involved in their designs, and truly want every facet understood, and thus appreciated, by their players. And I think that's fine - after the fact. During the actual adventure, they should be kept as ignorant as possible.
Which might be one of the principle reasons for the disconnect in my online games. I do intentionally withhold information. I do it constantly. I have elements in my campaigns that I have literally withheld for years. I shall give an example.
About two years ago, real time, my offline campaigners came across a caravan on the edge of the Ust Urt plateau(NW Turkmenistan), in which three ogres were transporting 17 women, none with a charisma less than 16. The party killed the ogres, freed the women, and discovered that many of them were from prestigious households throughout northern Persia. What followed was a lengthy adventure in which the women were returned.
The women, as it turned out, were a sacrifice planned by a high level mage by the name of Patroclus. Patroclus wasn't happy. But although he had every intention of frying the party down to the last member, the party returning the Emir of Tabiristan's daughter won them a special gift - a Libram of Proof Against Detection. As long as any member of the original party holds the Libram, they can't be found with ESP, Clairaudience or any other finding spell.
Now, the party has never seen Patroclus; they have been able to identify him as one of the Wizard Princes of a region called Khorezm (modern Khiva), but that's all. They have heard neither hide nor hair of him in eighteen months, but they know me and they haven't forgotten. Patroclus can still find them by that old tried and true method, investigation ... and though they've teleported once as a party since, there are still elements that can be identified. Sooner or later (and only I know when), Patroclus will find them.
But what happens then, I've never told anyone.
It is the same methodology applied to novel writing ... withhold, withhold, withhold. No character ever has more information than is absolutely necessary, no one in the novel ever knows everything that is going on except for the one character you don't get a chance to talk with until the very end. In D&D, the novel never ends. Whatever might get resolved, there have always been other aspects of the journey that have been created along the way, leading to other adventures and other resolutions, some soon, some much later.
In that way, yes, D&D is storytelling. Or rather, it is NOT storytelling. All too often, I think, the whole story gets told right at the beginning, and nothing is really a surprise - need the key, find the key, fight for the key, get the key.
Not telling the story begins, as I began, with not telling the players why you're rolling. Or why they're rolling. It's in the DMG and it's good advice. With some players, it will take time to break them of their "knowing all things" habit ... but your campaign will get better once you do.