No one told Draco before he received the Mark--indeed, no one could have told him--precisely what it is. He had thought it no more than a badge of membership, terrifying because of the immeasurable power the Death Eaters wielded. Now he knows better, and wishes he did not.
It's more than a magical tattoo. Infinitely more.
At its most basic level, it's a binding spell. He can feel the spell delicately intertwining with his magic, linking his power to that of the Dark Lord's. This sounds more impressive than it is, for Draco knows that he has no access to the Dark Lord's power. He, like the rest of the Death Eaters, is now no more than an ambulatory magical pool that he can draw upon. If he ever needs extra power to fuel his spells, the magic--and perhaps the lives--of the Death Eaters will fuel it.
And because it compels loyal behavior, or at least the semblance of it, he cannot call attention to the Dark Mark. He gathers from elliptical comments in his mother's letters that the spells have been reinforced of late, thanks to that pathetic fool Stan Shunpike's boasting of being a Death Eater to sound more impressive. He cannot even explain the Mark away if anyone asks; like all other Death Eaters now, he is bound to silence, save under the influence of Veritaserum. Only a Legilimens or Occlumens can weave a path around the silencing spell...and Draco knows he is neither.
It does not help to know that he and the other Death Eaters are better off than Shunpike, who suffered the full brunt of the Dark Lord's wrath. In punishment for his babbling, Shunpike has been cursed to endless silence, eternal illiteracy. He will never speak or write another word to another person so long as he lives.
Draco strives not to envision himself or his parents in Shunpike's place.
He takes steps to protect himself. He takes showers far earlier in the morning than his dorm mates. He wears heavy black woolen robes whose sleeves he enchants twice over: they will not roll up, exposing the Mark to all eyes, and they will not attract attention by refusing to roll up, either. He fights not to rub the Mark no matter how much it throbs and aches. Touching the accursed thing is like sending a private Floo message directly to the Dark Lord; to send him a message is to proclaim yourself his equal rather than his servant. Draco needs no one to tell him that such a proclamation--even if unintentional--would be suicide. He even tries enchanting his own skin to conceal the Mark from curious eyes...which is when he learns something interesting.
While the Dark Mark is visible to other Death Eaters and to potential victims, those in the Order can neither see it nor sense its presence. McGonagall and Dumbledore could stare at his Mark for the rest of eternity and would see nothing. If any of his classmates pointed his Mark out to them, they could cast every spell in Hogwarts' library, including Finite Incantatem, and they wouldn't sense the Mark's existence. In fact, they would probably become indignant or even protective, insisting that he was a helpless innocent at best, a wretched dupe at worst.
Even if events forced them to admit that he was aiding the Death Eaters, Draco is certain that they'd never believe that it was--or, rather had been, at one point--his choice. As long as the tattoo inks and his seared flesh bind the Dark Lord's enchantments into his body, the Mark--and its effects--will remain.
He dares not admit, even to himself, that he no longer wants to be a Death Eater. The Dark Lord has a habit of slicing into the minds of his followers at random times. Draco does not want to be thinking anything disloyal when the Dark Lord comes calling. The results of disloyalty are hideous...and only the mildest are fatal.
Throwing himself into his roles, Draco strives, simultaneously, to be a rich young man who is developing a few inexplicable albeit charming eccentricities (like wearing winter-thick robes in the last warm days of autumn), his normal arrogant Slytherin self, and a skilled young secret-agent assassin on his first--and quite possibly last--assignment. He spends much of his time trying not to think of what will happen if he fails, and he isn't sleeping much, but he thinks that most of the time, he's maintaining his multiple masks quite well.
Then one day over Christmas hols he attends a Death Eater meeting, and--as he strives to do anything but attract the Dark Lord's attention--accidentally glances at the Mudblood turncoat, Wormtail.
Wormtail is the lowest of the low. Contemptible. Loathsome. Dirt beneath the feet of purebloods. He knows better than to look at other Death Eaters for long. But for one moment, he gazes at Draco.
And Draco is staggered by the bleak pity in the older man's eyes.