Webster puts it nicely: Elevated in character or quality.
To be high, in modern parlance, is to be in an altered state of mind, usually by the influence of a substance. It is most commonly applied to the use of narcotics and marijuana, but can also be applied to opioids, hallucinogens (both synthetic and otherwise), and even alcohol, although this last use is unusual.
The use of this word should indicate that one has attained a plane of understanding elevated above that of the common, sober man. That is, one's outlook is clearer, one's powers of perception are greater, being unencumbered by the shadows of the mundane world. Obviously, "high" is not always an accurately applied term, unless eating a whole bag of Fritos and playing PlayStation for eight consecutive hours is said to be an "elevated character." Use of the word "high" in such a situation may be somewhat ironic in nature.
Some people are able to attain such an elevated character or quality without the use of a substance, and are said to be high on life.