The great Russian writer Leo Tolstoy wrote a thought-provoking book with exactly the same title as your question: What Is Art? The entire text of the book is accessible on the internet, since the work is old enough to be in the public domain. In the first chapters Tolstoy summarizes everything previously written about the definition of art that he considers important. Then in chapter five he offers his own definition of art as follows in full:
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--this 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.
I offer you this answer to your question as the best definition of art that I have ever encountered.
Many people have disagreed with Tolstoy's definition of art as the transmission of feelings and with many of the other things he has to say in his book. He has frequently been ridiculed and misinterpreted and misquoted. But he has some very important thoughts on the subject, regardless of whether or not he is entirely correct.
One of the most interesting parts of Tolstoy's book is the section in which he discusses what he calls "counterfeit art." He charges that professionalism in art led to insincerity and commerialism. He identifies four methods of producing counterfeit art: borrowing, imitating, striking (creating effects), and interesting. We can see these methods clearly in much of our contemporary "art," especially in our popular music and movies. In fact, many movies utilize all four of these methods of producing an effect on the audience which is not artistic but creates some kind of an impression on people which they may mistake for a transmission of real feelings. One means of "interesting" an audience in a movie is to shoot the film in a new location, so that many movies are something like dramas and travelogues combined. As far as creating effects, we are all too familiar with the explosions, car chases, shootouts, and scenes in which cars or motorcycles crash out of high-rise parking structures and fly through the air. The movies are so full of such effects that any time we see an actor get in a car and turn the ignition switch, we half-expect to see the car explode and burst into flames.
Tolstoy thought that the most important element in art was sincerity. He would be unlikely to think very much of what is presented as art in our time.