To ask what art is good for is not exactly the same as asking what its purpose is. Art does not have to have a purpose - it does not exist in order to teach, to urge a moral point, to entertain, to distract, to amuse, to serve beauty, to support a revolution, to disgust, to challenge, to stimulate or to cheer; it exists chiefly for its own sake. It is the artist, not art as such, that may have an aim in mind, and his aim may be to do any of the things just listed. But equally, an artist may just make art because he feels compelled to. Because the work is its own justification, no further aim or goal is necessarily required to explain or, still less, to justify its existence.
But to say that art does not have to serve an aim beyond itself, even though it may sometimes do so, is not to say that it is good for nothing. On the contrary, as one of the greatest goods of human experience, it is good for many things. The distinction here lies between things that are instrumental and things that are ends in themselves. An instrument exists for something beyond itself - namely, for what it can be used to do. An end in itself is its own justification for existing. Even though art can sometimes be instrumental, that fact is not essential to its nature. What art is "good for" arises from its being an end in itself, or more accurately, the embodiment of many different things that are valuable for their own sakes.
The word "art" does duty here for painting, sculpture, music, literature, dance and theatre performance, and whatever else (to quote Andy Warhol) anyone can get away with in calling it "art". But the generalisation that art, whatever else it is, is always an end in itself, applies to them all. This can be shown as follows.
Art is one major form of response to the world. It is often an attempt to capture an aspect of the world, to draw attention to something about it, to comment on it, to present a surprising or fresh angle on it, to represent it for the sake of exploring something about it, or enjoying or celebrating it - for example, the colours or shapes of an object, its eccentricity or typicality, the interest or repugnance it provokes.
For a loose comparison, think of laughing at a joke. We do not laugh so that we can achieve a further goal - in order to be healthy or relaxed, say, even if we thereby succeed in being healthier or more relaxed - but simply because the joke has elicited that reaction. But although it is merely a reaction, laughing is, in fact, good for something nevertheless; it does make people feel better. Art is a reaction in the same way. Cezanne painted Mont Sainte-Victoire repeatedly because he was fascinated by it, not because he thought that painting it would say something about politics or society or human hopes. Being fascinated by something, attracted to it, repelled by it, keen to reveal an unusual aspect of it, are all responses to that thing; the making of art is one outstanding way of expressing such responses.
But art is a response not only to things in the world but to experience of the world, which lies inside the artist himself. And it is also often an expression of what presses from within the artist without being elicited by externals. Music is a prime example. A symphony, unless it has a programme and is devised to represent bird song, rain, battle and the like, is an abstract expression of a composer's conception.
The impulse to make art, as with poetry, can result in the artist imparting a message, but the art lies not in the message but in the way it is conveyed. An interest in materials and techniques without any explicit content, as in abstract painting or contemporary dance, leads to a form of distinctively modern art that switches the focus of attention, as when people look at a frame rather than the picture within. It is still art, still an expression of a response to something within or without.
When artists get to work responding and expressing, whether or not also to urge a point, entertain, distract, support a revolution and the rest, they are producing something that someone else will react to in some way. And that is what art is chiefly good for: namely, that by its relationship with its audience it can make something move in the realm of thought and emotion, where such movement is life.