To express the things that are hard to express but are recognizable once they're expressed. To set down emotion in a lasting form. To commemorate. To show someone how it looks through the eyes of the heart, not just the eyes.
When I write down "I was driving through the city at night on the freeway and it smelled cold and sad" you don't feel what I felt. When I show how it was in words, my writing crowd was bowled over and felt if not the identical emotion, something similar.
It's a record of the intangible and the ephemeral. As a scientist, I was trained to work with the tangible and quantifiable and extract meaning from them. As an artist and magician, I was trained to manipulate the tangible and quantifiable to produce transcendence.
We are all shut in our little boxes of heads, and the moment of art is the reaching out between those and saying, "Yeah, I think I was there too." Art ties a society together beyond mere common memes.