What can’t language express? Well, language is ultimately very limited in communicating the incredibly intricate and specific experience that is being a human being. Even when describing things we are often liable to expressing things in a way our audience can't understand. No one is quite able to experience that same sunset in the same way, the colours appear different, the state of mind you watch it in can be different, our regional language or personal history changes how we perceive it. E.g., Russian speakers are much better at distinguishing shades of blue because they distinguish between the dark and light much more than we do in English, and likewise English speakers are much better at distinguishing certain types or shades of colour than German speakers because we have more words for it (i.e., magenta, cyan, aqua-marine, etc.).
In Zen as well (and most schools of Buddhism teach similar ideas), it's believed that the concept of zen cannot be taught at all through language and that any attempts to do so immediately betray the concept of Zen. Zen can only be experienced, not taught or communicated.
I read Siddhartha by Herman Hesse recently and the final chapter deals very eloquently with the dilemma of using a dualistic language to express nondualistic ideas, thoughts, or emotion ultimately engenders confusion and misundertsanding.
Edit: I'd meant to write this part earlier but forgot because it was pretty late. To expand on my thoughts on language, as a communicative device I do believe it is incapable of communicating the totality of how we feel or who we are. The very fact I have to add this part on and that I intend to clarify some of what I say in another post I think shows how language has its ineptitudes when it comes to expressing how we feel and what we think to others. All relationships are in some sense para-social, it is a one-sided and often one-dimensional exchange of information or parts of our beliefs or opinions to one another. It's practically impossible for anyone to know themselves, let alone know other people, not least because the language we use to convey ourselves to others is too fragmented and incomplete to express the totality and complexity of any given human being. Language is the performance if the belief, the idea, the feelings, not of any of these themselves. Language is a barrier unto itself, it is a performance, a recreation of the real in way that we hope are intelligible to others, it is not the real itself and therefore we can express the whole of what we feel and cracks begin to appear in our understanding.