It's my personal feeling that people who assert that modern and postmodern art are garbage (note: not the same as a person who just dislikes it) truly don't understand art as a whole. Should they have to? No, actually. But. They forfeit their right to speak authoritatively about it, IMO.
The heart of those movements are actually very simple to understand. Think about it like this: what is left of art when you take away a person's ability to draw in a representational manner? The rest of art-- all other elements they teach that make your representational work good-- art's elements and principals (line, value, composition, movement, rhythm, etcetc), and all emotional baggage, narrative and other storytelling devices.
A random person of the street doesn't understand how important these things are, and most often cannot appreciate them or understand what they are appreciating. Let's say he/she is magically handed the ability to draw objects in the world perfectly. Great, but what does he do with it now in order to create a striking, thought-provoking piece after that? Here's the difference:
A person who can just draw stuff is likely to produce something like this:

So great, they drew a person standing there. Yep. Looks like a person standing there.
A person who has all of the other skills that are heavily used in modern and postmodern movements produces things like this:

Because the artist knew to move the figure to the far edge of the picture plane, and emphasize all of that awkward white space a viewer suddenly has all of these questions-- is the person shy/hiding? What does the other half of them look like, and why aren't we allowed to see it? Is this person in the middle of an action, is that why they're not completely in the picture plane? Really, the possibilities are endless.
So modern/postmodern movements take this way further than my ten-second examples. XD;;
