To add to what krenseby has already said about the role of understanding and imagination in aesthetic judgment, I can offer a supplementary explanation of how imagination and understanding allow us to judge what is beautiful and what is sublime and, more generally, of what role beauty and the sublime play in Kantian philosophy.
The judgment of beauty is arational
For Kant, beauty begins with sensory experiences and a consciousness of the pleasure attained through them as they affect the understanding and imagination. His conception of beauty, then, is very distinct from that of Plato because in Kant’s view reason plays no part in apprehending the beautiful. Beauty is apprehended through an aesthetical judgment, not a rational one.
Sensation, Understanding, Imagination, and Reason
In order to understand how Kant arrives at this conclusion, one must be familiar with the terms he employs in his argument, especially the terms sensation, understanding, imagination, and reason which create the framework for experience. Sensation is the beginning of our experiences. We are first aware, not of things in space and time, but of the internal effect that they create in us, acting on us, as it were, through the senses. The second level of this framework is the understanding which builds a world of objective meaning out of mere sensation, sorting and ordering sensory data into coherent relationships according to universal principles. The imagination, the third level, unites the products of understanding under an “I,” a conscious agent to whom phenomena appear. Reason, the final aspect, is that which drives us to a completeness in our knowledge of the world and self. Furthermore, it moves us to see the unity in all things, to attempt to construct out of our many concepts and experiences a single illuminating principle.
Objects of "free beauty"
How does beauty fit into this matrix? Kant claims that beauty is available most clearly to us if it is independent of a sustaining concept. A sign of this is that we do not find any deeper appreciation in the beauty of a flower after years of botanical study. The flower does not suddenly become more beautiful once we understand how the parts are formed and interact, what chemicals operate in certain processes, whether the flower is a perennial or an annual, or any other piece of trivia. Dependent beauty, on the other hand, does require the knowledge of a certain concept to sustain the beauty of an object. It is difficult for me to think of an example of such an instance because for the “beauty” that one might associate with mathematical or scientific concepts, Kant employs the word “elegant.” Could a case can be made for the fractal? Understood as merely a pattern or a design, it has a sort of superficial beauty. Understood as a mathematical concept, the fractal—finite in area but infinite in the length of its perimeter, self-similar at arbitrary levels of magnification, yet expressed by a simple, recursive definition—may be called beautiful, although certainly mixed with elements of the sublime. But even if we went so far as to grant this as true, that mathematical understanding sustains the beauty of the fractal, we must admit that the beauty is less clearly expressed than the free beauty of the flower.
Beautiful objects of "disinterested satisfaction"
Not only is the flower an object of free beauty, it is an object of disinterested satisfaction; meaning that the beauty of the flower is not bound up in any ideas of utility or morality that affect our judgment of its beauty. There is really no reasoned explanation one can give for why he appreciates the aesthetic beauty of a flower—it is a question irresolvable by the intellect. What Kant calls the “Ideal of Beauty,” however, does pertain to an intellectual judgment. The Ideal of Beauty is an object which somehow presents morality—embodies it, gives it substance and tangibility. Therefore, an art piece which attempts to portray the Ideal of Beauty is necessarily judged in terms of a concept and is an example of dependent beauty. Also, the Ideal of Beauty is clearly not an object of disinterested satisfaction because one’s appreciation of it relies on a reasoned explanation.
Aesthetic judgments are analogous to moral judgments
Though there is no substitute seeing the beautiful firsthand, one can have an indirect, intellectual interest in the beautiful by studying the great works of past artists and trying to grasp the aesthetic values of the sensus communis. This kind of scholarship may have the benefit of cultivating moral sense in addition to aesthetic taste. According to Kant, aesthetic judgments are analogous to moral judgments for they are both underpinned by revelations of the supersensible. For this reason, he calls beauty “the symbol of morality.” Human conscience and human appreciation of beauty attest to an attunement to the divine.
The sublime
Likewise, human awareness of the sublime in nature is a felt moral relationship to the whole. This feeling of awe, insignificance, and stupefaction comes about when human thought approaches its limit. It is characterized by a tension between imagination and reason. Despite this psychic threat, something within us feels compelled to seek out sublime experiences—at least through the mediation of art. In this way, like beauty, it is an object of disinterested satisfaction. However, unlike beauty, it does not produce the harmonious free play between understanding and imagination. Beauty makes us feel “at home” in the universe and sublimity seems to challenge this notion severely. However, Kant claims that the sublime is that which wakes us up to our moral destiny and excellence as free, thinking, moral agents.