I've talked about this trope before. In a formulaic way, words cannot describe just means the experience is powerful. It really isn't about words themselves, but about experience. You expect me to say something, but any statement pales in proportion to the experience itself. "I have no words..." and then the speaker gives a speech anyway about having no words.
The next stage of the trope is to focus on language itself. Here, the point is that language is inadequate on some fundamental level. Inadequate for the enormous experience... but I would say also not really suited to evoke even ordinary life. I cannot make my words smell like cinnamon. If you already know what it smells like, then the word just functions as an arbitrary surrogate. If you don't know the smell, or if you don't know the word, then it doesn't work at all.
The third step in my argument is that this is not what language is supposed to do anyway. It was never supposed to be a surrogate for reality itself. It can only be judged inadequate because we have a false idea of what it's supposed to be. Take music. We can use language to notate music, but it is a bit awkward: a quarter note triplet played legato on G4. We have another system, called sheet music, that does the job better, though it is also awkward to read and write except for highly trained musicians. The sheet music is inadequate too, but good enough to preserve musical ideas and tell the performer how to realize them.
Here's where it gets interesting. Even though that is not the main job of language, language can be evocative also. It is no longer an abstract representation of reality, but an experience that is real in its own right. This is something that we call "poetry." The combination of words gives us something new, something that cuts through our ordinary perception with an intensity. Think of a poem that tries to talk about the experience of listening to Monk play. Ok. It will probably be a bad poem because it sets itself up to fail by trying to replicate an experience in an inadequate medium. Now think of a poem that is not about Monk but replicates the experience of his music in a different medium, adequate to itself.