For Kierkegaard, true individuality is called selfhood. Becoming aware of our true self is our true task and endeavor in life—it is an ethical imperative, as well as preparatory to a true religious understanding. Individuals can exist at a level that is less than true selfhood. We can live, for example, simply in terms of our pleasures—our immediate satisfaction of desires, propensities, or distractions. In this way, we glide through life without direction or purpose (see Kierkegaard on the Aesthetic, Ethical and Religious. To have a direction, we must have a purpose that defines for us the meaning of our lives. Kierkegaard puts it this way in Either/Or.
Here, then, I have your view of life, and, believe me, much of your life will become clear to you if you will consider it along with me as thought-despair. You are a hater of activity in life-quite appropriately, because if there is to be meaning in it life must have continuity, and this your life does not have. You keep busy with your studies, to be sure; you are even diligent; but it is only for your sake, and it is done with as little teleology as possible. Moreover, you are unoccupied; like the laborers in the Gospel standing idle in the marketplace, you stick your hands in your pocket and contemplate life. Now you rest in despair. Nothing concerns you; you step aside for nothing; “If someone threw a roof tile down I would still not step aside.” You are like a dying person. You die daily, not in the profound, earnest sense in which one usually understands these words, but life has lost its reality and you “Always count the days of your life from one termination-notice to the next.” You let everything pass you by; nothing makes any impact. But then something suddenly comes along that grips you, an idea, a situation, a young girl’s smile, and now you are “involved,” for just on certain occasions you are not “involved,” so at other times you are “at your service” in every way. Wherever there is something going on you join in. You behave in life as you usually do in a crowd. “You work yourself into the tightest group, see to it, if possible, to get yourself shoved up over the others so that you come to be above them, and as soon as you are up there you make yourself as comfortable as possible, and in this way you let yourself be carried through life.” But when the crowd is gone, when the event is over, you again stand on the street corner and look at the world. Either/Or Part II p. 195-196
In Sickness Unto Death specifically Kierkegaard deals with the self as a product of relations. In this sense, a human results from a relation between the Infinite (Noumena, spirit, eternal) and Finite (Phenomena, body, temporal). This does not create a true self, as a human can live without a "self" as he defines it. Instead, the Self or ability for the self to be created from a relation to the Absolute or God (the Self can only be realized through a relation to God) arises as a relation between the relation of the Finite and Infinite relating back to the human. This would be a positive relation. An individual person, for Kierkegaard, is a particular that no abstract formula or definition can ever capture. Including the individual in "the public" (or "the crowd" or "the herd") or subsuming a human being as simply a member of a species is a reduction of the true meaning of life for individuals. What philosophy or politics try to do is to categorize and pigeonhole individuals by group characteristics, each with their own individual differences. In Four Upbuilding Discourses, 1843 Kierkegaard says the differences aren't important, the likeness with God is what brings equality.
In the hallowed places, in every upbuilding view of life, the thought arises in a person’s soul that help him to fight the good fight with flesh and blood, with principalities and powers, and in the fight to free himself for equality before God, whether this battle is more a war of aggression against the differences that want to encumber him with worldly favoritism or a defensive war against the differences that want to make him anxious in worldly perdition. Only in this way is equality the divine law, only in this way is the struggle the truth, only in this way does the victory have validity- only when the single individual fights for himself with himself within himself and does not unseasonably presume to help the whole world to obtain external equality, which is of very little benefit, all the less so because it never existed, if for no other reason than that everyone would come to thank him and become unequal before him, only in this way is equality the divine law. Eighteen Upbuilding Discourses, by Soren Kiekegaard Hong, p. 143
Kierkegaard's critique of the modern age, therefore, is about the loss of what it means to be an individual. Modern society contributes to this dissolution of what it means to be an individual. Through its production of the false idol of "the public", it diverts attention away from individuals to a mass public that loses itself in abstractions, communal dreams, and fantasies. It is helped in this task by the media and the mass production of products to keep it distracted. Even the fight for temporal equality is a distraction. In Works of Love he writes:
To bring about similarity among people in the world, to apportion to people, if possible equally, the conditions of temporality, is indeed something that preoccupies worldliness to a high degree. But even what we may call the well-intentioned worldly effort in this regard never comes to an understanding with Christianity. Well-intentioned worldliness remains piously, if you will, convinced that there must be one temporal condition, one earthly dissimilarity – found by means of calculations and surveys or in whatever other way – that is equality. Works of Love, by Soren Kierkegaard, 1847, Hong 1995 p. 71-72 see p. 61-90
Although Kierkegaard attacked "the public", he is supportive of communities:
In community, the individual is, crucial as the prior condition for forming a community. … Every individual in the community guarantees the community; the public is a chimera, numerality is everything… — Søren Kierkegaard, Journals[