He had to clap his hands to his mouth to stop himself from screaming. He whirled around. His heart was pounding far more furiously than when the book had screamed—for he had seen not only himself in the mirror, but a whole crowd of people standing right behind him...
They just looked at him, smiling. And slowly, Harry looked into the faces of the other people in the mirror, and saw other pairs of green eyes like his, other noses like his, even a little old man who looked as though he had Harry's knobbly knees—Harry was looking at his family, for the first time in his life.
The Potters smiled and waved at Harry and he stared hungrily back at them, his hands pressed flat against the glass as though he was hoping to fall right through it and reach them. He had a powerful kind of ache inside him, half joy, half terrible sadness. (Harry Potter and the Sorcerer's Stone, pg 208-9).
Although J. K. Rowling probably did not intend it, the quoted passage neatly allegorizes the alienation that contemporary children face with regard to their parents, summed up in real life by this platitude: "My parents don't understand me."
The conflict that underlies this alienation has always existed; it is rooted in the differences between the value systems of adults and children. Humans are not born with any values system; if they are to have one, it must be acquired. If the children progress to the point where they have gained their parents' outlook on life, the conflict fades away.
As little as a century ago it was the universal expectation that children would adopt their parents' values, and thereby become adults themselves. As the apostle Paul writes, "When I was a child, I spake as a child, I understood as a child, I thought as a child; but when I became a man, I put away childish things." (1 Cor 13:11) It was expected that children would behave differently from adults, but it was also expected that they would cross the generation gap; the child who rebelled was in the wrong. To suggest that children need not grow into their parent's outlook was viewed as an attack on society, to which the ghost of Socrates can bear witness.
This greatly contrasts with modern society, which is at best indifferent to the generation gap. Children are no longer expected to recognize that it is their lack of maturity which sets them apart from their parents; rather they are permitted, if not encouraged, to think that their parents follow an old and outdated set of ideas, which they need not accept. Furthermore, children are encouraged to believe that they are betraying themselves if they adopt their parents' values, thereby freezing a passing state of disagreement into a durable state of alienation.
As a result, contemporary children feel irremediably cut off from their parents. This is not without consequence: Children need their parents, even if they have been taught to pretend otherwise, and any separation from a loved one is painful. They are offered pop culture as a substitute, but it is profoundly inadequate; the pain edures.
This theme is presented allegorically with the Mirror of Erised. The allegory is not perfect; no allegory is. Harry's separation from his parents is physical, rather than philosophical. He is not in denial of the cause of his pain, and he has rejected utterly the idea that he is better off without his parents. Furthermore, contemporary children bear a small responsibility for their slowness to adopt their parents' values, whereas the death of Harry's parents was none of Harry's doing.
Nonetheless, the allegory is apt. He is cut off from the people that love him without reservation. He has the worldly benefit of their parentage—fame and wealth—but it is meaningless to him. He has no father with whom he can talk about Cho Chang, no mother for whose gaze he can hold up the hard-gained Snitch at the end of a Quidditch match. In #4 Privet Drive, and in the corridors of Hogwarts, Harry can put these things out of mind; before the Mirror, Harry has no choice but to feel the love that could have been, and the pain from knowing that this love can never be expressed; and among our alienated youth there are countless children who read this passage and say to themselves, "this is how I feel."