Why are Picasso paintings so important? How can I appreciate the importance of
I'm no expert on art, just someone who enjoys it, but I certainly would agree with you that Picasso can be hard to understand. Most of his painting (and sculpture) isn't what one would describe as "beautiful", though there are paintings of his that are beautiful: For example, "Child with a Dove" (see it here). But what's beautiful about paintings like this one, to my mind, is what they convey emotionally and less anything to do with sheer physical beauty. And one finds a similar sort of emotional intensity in many of Picasso's other works. His portrait of Gertrude Stein (here) is just brilliant.
Now, to be sure, Picasso's later works can be more challenging. It can be very hard even to see what's happening in paintings like "The Guitar Player" (here) or "Afficionado" (here). And, in this case, I think it can help a great deal, as one tries to learn how to see these paintings, to learn something about the aesthetic that lies behind them. Picasso did not decide to paint in the ways he did simply out of perversity. He was looking for a way to express things he could not otherwise express. (Schoenberg makes similar remarks about the reasons for his invention of the twelve-tone method of composition.) How much success Picasso had is presumably for the viewer to judge. But once one opens one's mind, and better one's heart, to what Picasso is trying to do, one can come to see a painting like "Portrait of Maya with a Doll" (here) as, indeed, quite beautiful.
For me, though, the proof of Picasso's genius is the single painting "Guernica" (here). No more powerful comment on the horrors of war has ever been produced, and I can't even begin to see how Picasso could have produced such a powerful piece of work except by marshalling everything he had done beforehand. If you are ever in Madrid, you really must see it. It's exhibited along with many of the studies Picasso did as preparation, and it is fascinating to see the vision finally emerge.