To understand abstract art, you have to realise that Art has a cognitive function. Quite separate to its illustrative, commercial and political applications.
Something like the relationship that exists, between pure scientific research, (that most of us don’t understand), and the technological spinoffs from that research, that we all enjoy.
Most of the conventions we see in Movies, illustration, CG, comics, advertising, everywhere. All make use, of discoveries made by artists, centuries ago. For example: ‘one point perspective’ discovered during the Renaissance. Controposto, see Michaelangelo ‘David’, Leonardo’s Use of chiaroscuro (light and shade), and his discovery of the effect of using a 3 quarter view of the head, in portraiture. ‘The Golden section’, what many here know as the rule of thirds. And many other compositional devices that are in common, almost automatic usage today, were all discovered during the 15th century.
You see Art, just like Science, Philosophy and Theology, is something that human beings use, to create metaphors for reality. And the goal of art at that time was realism.
So, once the artistic representation of reality reached a zenith, did artists just stop, give themselves a pat on the back and say ‘yes that’s it. We’ve done it’. Not likely. Some realised it still was not good enough, that there is a lot more to reality, than describing a surface. After all no one ever walked into a room, looked at a painting and said, " Wow! I thought that was a real six inch high woman pouring milk into a bowl" (in this case"The Kitchen Maid" by Vermeer):
http://www.rijksmuseum.nl/aria/aria_assets/SK-A-2344?lang=en
It’s more than 15 years since I graduated, so for the moment I just can’t remember the name of the artist who toward the end of the 19th century. First noted that all paintings are abstract, no matter what you do, they remain no more than ‘arrangements of colour next to one another’. If that’s what a painting is, the challenge for some is to see what a painting can do, so to speak.
While most of what we see in every day use around us today, borrows ideas from the 15th century. Artists like Braque and Picasso early in the 20th century, were using multiple perspective views and multiple positions in time, in their images. Ideas paralleled by the Scientific thinking of the time, notably Einstein’s theories concerning simultaneity and relativity.
Artists are still engaged in visual research. It’s not always pretty or nice. But there are very often universal benefits to gained from the risks taken, and insights gained by artists engaged on that path.