[handrous]

The language takes some getting used to. Watching a performance is easier than reading it, since (again) you have the context of the actor's physical performance, delivery, the setting of the scene, et c., to inform your understanding. Another thing is that often his plays rely on some historical understanding for full effect. For example, most people reading the beginning of Hamlet might not fully grasp what's going on, while someone with a good understanding of feudal politics (or anyone who's played much Crusader Kings) will be going "oh shit, this is really bad". This is where something like Asimov's guide to Shakespeare, or any number of free online lectures about the plays, can be helpful.

As for what's great:

1) Masterful plotting, leaving just enough up to the audience to figure out (and, more often than not, leveraging that for ironic purposes).

2) Outstanding characterization.

3) A hard-to-pin-down quality that makes relating episodes, characters, and exchanges in his plays to real life the most natural thing in the world. There's a reason we've ended up with so many of his characters and phrases as parts of the English language itself.