#1 Kant believes that the world as we experience it is full of what he calls "representations." Thus when I look at a work of architecture I have a representation of it in my mind. The representation in what I see, not the thing as it is in itself. Now when I judge something as being beautiful or ugly, i.e. make a judgement of taste, something different happens than when I make a scientific judgment. I actually refer that representation to my feelings of pleasure or pain and judge accordingly: if it gives me pleasure I judge it as beautiful, and if it gives me pain, as ugly. So a judgment of taste is not objective but subjective. However this is merely a preliminary point and we will soon discover that Kant does not mean the same thing by "subjective" as we might. Here the emphasis is on not applying concepts of the understanding: not trying to analyze or classify. It is one thing to judge a building cognitively and another to judge it in terms of taste. Kant says that in taste we refer the representation to our "feeling of life, under the name of the feeling of pleasure of pain" and that the representation is being compared to "the whole faculty of representations, of which the mind is conscious in the feeling of its state." This seems to mean that in finding a building beautiful we are also conscious of the state of mind we are in, i.e. in terms of imagination and understanding. Later, he will observe that this state of mind involves the free play of these faculties.
#2 We next learn that the satisfaction is disinterested. That is, we are not to think of whether or not the object meets some personal need of ours. This idea expands Hume's notion that a good judge lacks prejudice. In Kant's case we cannot appreciate something as beautiful if it is in some way an object of desire, for example of sexual desire, or even of consumerist desire. "Interested" appreciation is going to be appreciation that cares about whether the object exists. For example one might care about whether the object can be mine or be used by me. Or one might care about the moral implications of the object in terms of social structure. Take a palace. Some people will judge the palace from an interested perspective. For example, they might judge it as being immoral insofar as it rests on the exploitation of the lower classes. Rousseau would say that it represents the vanity of the great. Kant approves of Rousseau's moral stance. But when it comes to appreciation of the palace one ought to be disinterested in its contemplation. Set aside issues of morality. The question is simply whether the mere representation of the palace in my mind (i.e. the image of it before me) gives me pleasure. Also, unlike the Iroquois sachem visiting Paris (Kant shows no appreciation of the sophistication of Iroquois culture here), one finds more aesthetic interest in other things than the restaurants. The restaurants provide sensual satisfaction and the actual existence of the food is important to us (we would be unhappy if the steak turned out to be a mere illusion). With matters of taste however the question is not how I can use the object but what I make out of it in my contemplation of it.
#3 Kant here distinguishes between different senses of "sensation": objective and subjective. The main point of the exercise is to distinguish between "impressions of sense which determine the inclination, fundamental propositions of reason which determine the will...[and] mere reflective forms of intuition which determine the judgment." These just aren't the same when it comes to the feeling of pleasure. You cannot accuse someone of moral baseness if all action is a matter of gratification. The feeling of pleasure is a sensation in a different sense from the representation of a thing. The first refers to the subject, the latter to the object. So, for the purposes of clarity, he calls what is always subjective "feeling." The example that helps here is the green color of the meadow. Its greenness belongs to objective sensation, its pleasantness to subjective. Further, if I consider something pleasant I have an interest in it. The sensation "excites a desire for objects of that kind." It has therefore a relation to my own existence. So the pleasant gratifies, and in its most lively form, this involve no judgment.