First of all, an artist has perspective.
Of course everyone has perspective, but the artist has perspective in two important ways. The artist sees a vision that most others don't see. Everyone looks at the same situation, yet the artist sees something in it that the others just simply do not see. This sets the artist apart, but not by choice. Also, the artists sees vivid actualities in life. It is comic, or it is tragic. It is exhilarating, or crushing. It is beautiful, or hideous. The artist sees that everything has a story, and he wonders what that story is. This unique and riveting viewpoint is the inspiration for art.
Secondly, an artist desires that others would see it too
The artist who sees all this is moved by it, and wants to share the experience with others. As I said, the artist is set apart from the group, but not by choice. The visionary would much rather that everyone sees what he sees! Like children playing "I spy", or the Christmas Carol "Do You See What I See?," the artist experiences something amazing, and just wants others to experience it too.
The artist must develop an artform
Now of course, any person who tried to share a vision will often come across the frustration of others just not getting it. You look out the window and catch a glance of a beautiful, majestic, and electrifying sunset. It takes you almost by surprise, and it sweeps you off your feet so that you excitedly call over your friend to see. But they look at it, and see nothing special. "The sun sets every day. So what? It's overrated." Then they turn and go back to what they were doing. That person has seen the sight, but not the vision. The colors were plain to them, but not the beauty or power of the scene.
This is the third part of being an artist: experiencing the frustration of have a vision and wanting to share it, but not being able to share that vision. That frustration is so ongoing and powerful that it motivated artists to spend hours upon hours, for years, developing a set of skills to be able to show others the vision. Some show visually by painting, drawing, or photography. By coloring and size and focus they show you what they see. Some compose moving music which expresses happiness, rapt, fear, heartbreak, or denouement. Others refine their skills at painting word pictures. C.S. Lewis and Chesterton both were very good at word pictures. Even if you do not agree with their conclusion, you feel that you have seen what they see in it. What is art, then? Art is a reflection, expression, or representation of something breathtaking. (For even tragedy can have a haunting beauty to it) Art is the means by which we communication these visions.
Finally, the artist cares more for beauty itself than for the appreciation of it.
Beauty should exist just for the sake of existing. It is better that a castle stand tall and beautiful where no one ever sees it than for it not to exist at all. This often comes across in the person's work. Who would put an extra two hours into details of a final masterpiece that no one will ever notice? Only the artist. Only the artist cares that much for the piece of work. I have often put in thought and time and hours making things awesome, knowing that no one will ever notice or appreciate it. A friend notices this, and asked if I was a perfectionist, but I am not at all.
Upon reflection, I realized that from an outsiders point of view, artists who spend those extra hours refining the work seem amazingly similar to perfectionist who spend extra hours making whatever it is perfect. But the motivation is completely different. A perfectionist is almost the opposite of an artist. Let me explain. The perfectionist is driven by dislike of what he sees. The writing is not perfect. He sees that. He does not like that. The force behind all his action is the feeling of dislike. On the other hand, the artist is driven by the vision he is trying to represent. Looking at a piece of rock, he sees the potential for a "David." He likes that vision, and is driving to make the real life rock more like the vision he sees in his mind. The artist is driving by liking what he sees. One can see at once the difference between these two mindsets!
Many times, a true artist will not create art for any particular reason, use, or purpose. It's just enjoyable for him. My brother, Silas, he makes music because it's beautiful and fun. He enjoys it. Beauty for the sake of beauty. So what if it's not profitable or popular? Those details matter not to the one who loves art for itself. Art may not help us survive in the world. It may not always have survival value. It's deeper than that, actually. Beauty and art is what gives value to survival! Beauty does not primarily help us to live. Beauty primarily gives us a reason to live. The artist sees this.
So, my conclusion is that many people make art, not all are truly artists. Bunches of people just make art for the money, or for other advantages that come with it. A person who is at heart an artist has vision, loves beauty for being itself, and desires to share the beauty they see with other people.