Leo Tolstoy, author of War and Peace, wrote a book titled What Is Art? in which he defines art and explains why art is of such importance to humanity. Here is his definition and a small part of his explanation of art's social importance.

To evoke in oneself a feeling one has once experienced, and having evoked it in oneself, then, by means of movements, lines, colors, sounds, or forms expressed in words, so to transmit that feeling that others may experience the same feeling--that is the activity of art.

Art is a human activity consisting in this, that one man consciously, by means of certain external signs, hands on to others feelings he has lived through, and that other people are infected by these feelings and also experience them.

If people lacked this capacity to receive the thoughts conceived by the men who preceded them and to pass on to others their own thoughts, men would be like wild beasts, or like Kaspar Hauser.

And if men lacked this other capacity of being infected by art, people might be almost more savage still, and, above all, more separated from, and more hostile to, one another.

And therefore the activity of art is a most important one, as important as the activity of speech itself and as generally diffused.   

Tolstoy believed that much of what passed for art in his time was really what he called counterfeit, and in his book he gives numerous examples of counterfeit art in literature, painting and music. He explains how counterfeit art is produced and the motivations for producing it, which are mainly economic. In his opinion, the most important quality of real art is sincerity, and this is what is always lacking in counterfeit art.

In our own times we have a great deal of counterfeit art which is especially conspicuous in movies and in popular music but also in so-called "fine art" and elsewhere.

Tolstoy's book, which bears the same title as your question, is well worth reading, since Tolstoy was such a great artist himself. Please consult the reference links below.

Broadly (historically) speaking, art is generally understood to be the use and application of imagination to create objects and experiences that can be shared with others. Today, art is more specifically described as objects and experiences created for aesthetic, emotional, intellectual, and symbolic effect. The historical concept of art used to be much more broad, including things like the “medical arts.” Modern topics on art tend to focus on disciplines such as music, painting, sculpture, literature, dance, theater, film, and opera.

In the case of the more ancient, historical definition, since art was defined as any skill, we could be talking about medicine, architecture, military strategy, etc.

Some scholars suggest that the idea of art as a creative practice emerged in its Modern conception during the Romantic period which was in the wake of the rational and logical movement called the Enlightenment. The shift during this period focused more on individual creativity and emphasized emotion and imagination. Some still regard art in its broader perspective of art as any “skill” and in this sense, art can include anything from woodworking to painting to computer design. In fact, Steve Jobs' contribution to the development at Apple was to synthesize art and technology.

The way art contributes to a society depends on the social context, the artist's intent, the art object's reception by the public, the genre, form, and subject matter.

Art is most generally a form of communication. This communication can have the intention (or effect, intended or unintended) to propose social/political change, it can symbolize religious figures/ideas, it can be a Realist reflection of real life, it can symbolize dreams and the unconscious (Surrealism). Art can also be “art for art's sake." This usually means more attention is paid to the form of art; not so much its subject matter. This is “art about art.”

Art can challenge social policies and it can explore psychological depths. Because artists use creativity and explore different ways of perceiving, art makes life potentially more rich and more profound because it implores us to consider aspects of our lives (and art itself) from alternative perspectives. For example, 1984 is George Orwell's warning about a bleak future where the government has suppressed individuality. 1984 is a novel, an art form which challenges readers to consider whether or not their own societies have similarities or show signs of developing towards such a scary future scenario. Another example is Pablo Picasso whose work redefined what could be done with the plastic arts and painting (the form) but also treated the subject matter of perception.

Art is the creative process of art objects, the objects themselves and the shared experiences of artists and the public. Depending on the form, context, subject matter, and communicative ability, art can induce one to contemplate the history of art itself as well as other aspects of human life such as personal experience, social structures, spirituality, and perception. Because art is a sensory experience, its medium is perception. This focus on perception calls attention to the ways we experience the world but it can also challenge us to consider other ideas and other ways of experiencing the world; and this reconsideration is not limited to sensory experience. It also can induce one to consider other personal, social, even technological aspects of how humans interact.