There are anti-apparition and anti-disapparition charms in Hogwarts before the Death Eaters took over.
During the Battle of Hogwarts the school enhanced the magical enchantments that protected the school. Then later Voldemort used the Elder Wand, the most powerful wand in existence. He used that wand to destroy the magical barrier in an instant, including the anti-apparition and anti-disapparition charms.
But because Voldemort didn't earn the wand, he was forcing it to utilize it's power which was causing it to break, and if he kept it up the wand would broke into pieces. It was powerful in its own right, but as Voldy said, it was holding back its power.
Anyway, Draco only apparates AFTER Voldy uses the Elder Wand and destroys the protective enchantments.
So in short, Draco could apparate because Voldy got rid of the magical protective charms.