There are several ways we put a value on art. The first way is simply material value. A particular piece of art may be considered valuable because of the material used in creating it. For example, the ancient Egyptians frequently used gold to represent the sun and divinity. Ancient Greek artists used bronze. This was valuable not simply because of the way it looked, but because these pieces of art could be melted down and formed into weapons if the need arose. .
Another value we put on art is intrinsic value. This depends mostly on the evaluation of the artist and the character of the work itself. An example of this is Leonardo DaVinci's Mona Lisa. Unlike the works described above, the Mona Lisa is composed of inexpensive materials, i.e. paint and wood. The artist was recognized as a genius by the people and his works have stood the test of time.
We also place value on art for religious reasons. Sculptures and paintings of religious figures make them accessible and put a visual image along with the idea or belief. Elaborate tombs depict life after death in some cultures. Stories from the Bible were communicated more effectively to people that were basically illiterate by various forms of art: paintings, mosaics, sculptures, and the like. This enabled the people to better grasp the teachings of the Bible by giving them something visual to relate to.
Art has Nationalistic value also. This means that the art conveys a particular culture's pride and/or accomplishment. The triumphal arches of ancient Rome is a prime example. These arches were "gateways" for victorious soldiers returning from war. Changes in world politics also can be an expression of the nationalistic value of art. When the Cold War ended, Russia sent various works of art to tour museums in the United States. Such a thing would never have occurred prior to this.
Finally, we place psychological value on art. Our reactions to art affect the entire range of human emotion.